R S AGGARWAL AND V AGGARWAL Solutions for Class 9 Maths Chapter 18 - Mean, Median and Mode of Ungrouped Data

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Chapter 18 - Mean, Median and Mode of Ungrouped Data Exercise MCQ

Question 1

If the mean of x, x+2, x+4, x+6 and x+8 is 11, the value of x is

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Solution 1

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 2

If the mean of x, x + 3, x + 5, x + 10 is 9, the mean of the last three observations is

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Solution 2

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 3

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Solution 3

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 4

If each observation of the data is decreased by 8 then their mean

(a) remains the same

(b) is decreased by 8

(c) is increased by 5

(d) becomes 8 times the original mean

Solution 4

Correct option: (b)

If each observation of the data is decreased by 8 then their mean is also decreased by 8. 

Question 5

The mean weight of six boys in a group is 48 kg. The individual weights of five them are 51 kg, 45 kg, 48 kg and 44 kg. The weight of 6th boy is

  1. 52 kg
  2. 52.8 kg
  3. 53 kg
  4. 47 kg
Solution 5

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 6

The mean of the marks scored by 50 students was found to be 39. Later on it was discovered that a score of 43 was misread as 23. The correct mean is

  1. 38.6
  2. 39.4
  3. 39.8
  4. 39.2
Solution 6

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 7

The mean of 100 items was found to be 64. Later on it was discovered that two items were misread as 26 and 9 instead of 36 and 90 respectively. The correct mean is

  1. 64.86
  2. 65.31
  3. 64.91
  4. 64.61
Solution 7

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 8

The mean of 100 observations is 50. If one of the observations 50 is replaced by 150, the resulting mean will be

  1. 50.5
  2. 51
  3. 51.5
  4. 52
Solution 8

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 9

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Solution 9

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 10

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Solution 10

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 11

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Solution 11

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 12

The mean of the following data is 8

X

3

5

7

9

11

13

Y

6

8

15

P

8

4

The value of p is

  1. 23
  2. 24
  3. 25
  4. 21
Solution 12

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 13

The runs scored by 11 members of a cricket team are

15, 34, 56, 27, 43, 29, 31, 13, 50, 20, 0

The median score is

  1. 27
  2. 29
  3. 31
  4. 20
Solution 13

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 14

The weight of 10 students (in kgs) are

55,40,35,52,60,38,36,45,31,44

The median weight is

  1. 40 kg
  2. 41 kg
  3. 42 kg
  4. 44 kg
Solution 14

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 15

The median of the numbers 4,4,5,7,6,7,7,12,3 is

  1. 4
  2. 5
  3. 6
  4. 7
Solution 15

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 16

The median of the numbers 84,78,54,56,68,22,34,45,39,54 is

  1. 45
  2. 49.5
  3. 54
  4. 56
Solution 16

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 17

Mode of the data 15,17,15,19,14,18,15,14,16,15,14,20,19,14,15 is

  1. 14
  2. 15
  3. 16
  4. 17
Solution 17

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 18

The median of the data arranged in ascending order

8, 9, 12, 18, (x +2), (x + 4), 30, 31, 34, 39 is 24. The value of x is.

  1. 22
  2. 21
  3. 20
  4. 24

 

Solution 18

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Chapter 18 - Mean, Median and Mode of Ungrouped Data Exercise Ex. 18A

Question 1(iv)

Find the arithmetic mean of:

All the factors of 20

Solution 1(iv)

Factors of 20 are: 1,2,4,5,10,20

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

        R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 1(iii)

Find the arithmetic mean of:

The first seven multiple of 5

Solution 1(iii)

First seven multiples of 5 are: 5,10,15, 20, 25, 30, 35

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Therefore, Mean =20

Question 1(ii)

Find the arithmetic mean of:

The first ten odd numbers

Solution 1(ii)

First ten odd numbers are:

1,3,5,7,9,11,13,15, 17, and 19

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 1(i)

Find the arithmetic mean of:

The first eight natural numbers

Solution 1(i)

first eight natural numbers are:

1,2,3,4,5,6,7and 8

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 1(v)

Find the mean of:

all prime numbers between 50 and 80.

Solution 1(v)

Prime numbers between 50 and 80 are as follows:

53, 59, 61, 67, 71, 73, 79

Total prime numbers between 50 and 80 = 7

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 2

The number of children in 10 families of a locality are

2,4,3,4,2,0,3,5,1,6.

Find the mean number of children per family.

Solution 2

Question 3

The following are number of books issued in a school library during a week:

105, 216, 322, 167, 273, 405, and 346.

Find the average number of books issued per day.

Solution 3

Sol.3

Question 4

The daily minimum temperature recorded (in degree F) at a place during a week was as under:

Monday

Tuesday

Wednesday

Thursday

Friday

Saturday

35.5

30.8

27.3

32.1

23.8

29.9

Find the mean temperature.

Solution 4

Question 5

If the mean of five observations x, x + 2, x + 4, x + 6, x + 8 is 13, find the value of x and hence find the mean of the last three observations.

Solution 5

Total numbers of observations = 5

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Thus, last three observations are (9 + 4), (9 + 6) and (9 + 8),

i.e. 13, 15 and 17

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 6

The mean weight of 6 boys in a group is 48 kg. The individual weights of five of them are 51 kg, 45 kg, 49 kg, 46 kg and 44 kg. Find the weight of the sixth boy.

Solution 6

Mean weight of the boys =48 kg

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Sum of the weight of6 boys =(48x6)kg =288kg

Sum of the weights of 5 boys=(51+45+49+46+44)kg=235kg

Weight of the sixth boy=(sum of the weights of 6 boys ) - (sum of the weights of 5 boys)

=(288-235)=53kg.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 7

The mean of the marks scored by 50 students was found to be 39. Later on it was discovered that a score of 43 was misread as 23. Find the correct mean.

Solution 7

Calculated mean marks of 50 students =39

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data calculated sum of these marks=(39x 50)=1950

Corrected sum of these marks

=[1950-(wrong number)+(correct number)]

=(1950-23+43) =1970

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Datacorrect mean =R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 8

The mean of 24 numbers is 35. If 3 is added to each number, what will bethe new mean?

Solution 8

Let the given numbers be x1,X2......X24

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 9

The mean of 20 numbers is 43. If 6 is subtracted from each of the numbers , what will be the new mean ?

Solution 9

Let the given numbers be x1, x2.....x20

Then , the mean of these numbers =

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 10

The mean of 15 numbers is 27. If each numbers is multiplied by 4, what will be the mean of the new numbers ?

Solution 10

Let the given numbers be x1, x2.......x15

Then the mean of these numbers=27

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 11

The mean of 12 numbers is 40. If each number is divided by 8, what will be the mean of the new numbers?

Solution 11

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 12

The mean of 20 number is 18. If 3 is added to each of the first ten numbers , find the mean of the new set of 20 numbers.

Solution 12

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

 

Question 13

The mean of six numbers is 23 . If one of the numbers is excluded , the mean of the remaining numbers is 20. Find the excluded number.

Solution 13

Mean of 6 numbers = 23

Sum of 6 numbers =(23x6 )=138

Again , mean of 5 numbers =20

Sum of 5 numbers=(20x 5 ) =100

The excluded number= (sum of 6 numbers )-(sum of 5 numbers)

=(138-100) =38

The excluded number=38.

Question 14

The average height of 30 boys was calculated to be 150 cm. It was detected later that one value of 165 cm was wrongly copied as 135 cm for the computation of the mean. Find the correct mean.

Solution 14

Mean height of 30 boys = 150 cm

Total height of 30 boys = 150 × 30 = 4500 cm

Correct sum = 4500 - incorrect value + correct value

= 4500 - 135 + 165

= 4530

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 15

The mean weight of a class of 34 students is 46.5 kg. If the of the teacher is included, the mean rises by 500 g. Find the weight of the teacher

Solution 15

Mean weight of 34 students = 46.5 kg

Total weight of 34 students =(34x46.5)kg =1581 kg

Mean weight of 34 students and the teacher =(46.5+0.5)kg=47kg R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped DataTotal weight of 34 students and the teacher

=(47x35)kg =1645kg

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data Weight of the teacher =(1645-1581)kg= 64kg

Question 16

The mean weight of a class of 36 students is 41 kg. If one of the students leaves the class then the mean is decreased by 200 g. find the weight of the student who left.

Solution 16

Mean weight of 36 students = 41 kg

Total weight of 36 students = 41x 36 kg = 1476kg

One student leaves the class mean is decreased by 200 g.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data New mean =(41-0.2)kg = 40.8 kg      R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Total weight of 35 students = 40.8x35 kg = 1428 kg.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Datathe weight of the student who left =(1476-1428)kg =48 kg.

Question 17

The average weight of a class of 39 students is 40 kg . When a new student is admitted to the class , the average decreases by 200 g . find the weight of the new student.

Solution 17

Mean weight of 39 students =40 kg

Total weight of 39 students = 40x 39) = 1560 kg

One student joins the class mean is decreased by 200 g.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data New mean =(40-0.2)kg = 39.8 kg               R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Total weight of 40 students =(39.8x40)kg=1592 kg.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Datathe weight of new student

= Total weight of 40 students - Total weight of 39 students

= 1592-1560 = 32 kg

Question 18

The average weight of 10 oarsmen in a boat is increased by 1.5 kg when one of the crew who weighs 58 kg is replaced by a new man . find the weight of a new man.

Solution 18

The increase in the average of 10 oarsmen = 1.5 kg

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped DataTotal weight increased =(1.5x10) kg=15 kg

Since the man weighing 58 kg has been replaced,

 Weight of the new man =(58+15)kg =73kg.

Question 19

The mean of 8 numbers is 35 . if a number is excluded then the mean is reduced by 3 . find the excluded number.

Solution 19

Mean of 8 numbers=35

Total sum of 8 numbers = 35x8 = 280

 Since One number is excluded, New mean = 35 - 3 = 32

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped DataTotal sum of 7 numbers = 32x7 = 224

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Datathe excluded number = Sum of 8 numbers - Sum of 7 numbers

= 280 - 224 = 56

Question 20

The mean of 150 items was found to be 60. Later on , it was discovered that the values of two items were misread as 52 and 8 instead of 152 and 88 respectively. Find the correct mean.

Solution 20

Mean of 150 items = 60

Total Sum of 150 items = 150x60 = 9000

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped DataCorrect sum of items =[(sum of 150 items)-(sum of wrong items)+(sum of right items)]

= [9000 - (52 + 8) + (152 + 88)]

= [9000-(52+8)+(152+88)]

= 9180

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data Correct mean =R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 21

The mean of 31 results 60. If the mean of the first 16 results is 58 and that of the last 16 numbers is 62, find the 16th result.

Solution 21

Mean of 31 results=60

Total sum of 31 results = 31x60 = 1860

Mean of the first 16 results =16x58=928

Total sum of the first 16 results=16x58=928

Mean of the last 16 results=62

Total sum of the last 16 results=16x62=992

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped DataThe 16th result = 928 + 992 - 1860

                          = 1920 - 1860 = 60

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped DataThe 16th result  = 60.

Question 22

The mean of 11 numbers is 42. If the mean of the first 6 numbers is 37 and that of the last 6 numbers is 46 . find the 6th number.

Solution 22

Mean of 11 numbers = 42

Total sum of 11 numbers = 42x11 = 462

Mean of the first 6 numbers = 37

Total sum of first 6 numbers = 37x6 = 222

Mean of the last 6 numbers = 46  

Total sum of last 6 numbers = 6x46 = 276

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped DataThe 6th number= 276 + 222 - 462

                          = 498 - 462 = 36

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped DataThe 6th number = 36

Question 23

The mean weight of 25 students of a class is 52 kg . If the mean weight of the first 13 students of the class is 48 kg that of the last 13 students is 55 kg . find the weight of the 13th student.

Solution 23

Mean weight of 25 students = 52kg

Total weight of 25 students = 52x25 kg=1300 kg

Mean of the first 13 students = 48 kg

Total weight of the first 13 students = 48x13 kg = 624kg

Mean of the last 13 students = 55 kg

Total weight of the last 13 students = 55x13 kg = 715 kg

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped DataThe weight of 13th student

= Total weight of the first 13 students +  Total weight of the last 13 students - Total weight of 25 students

= 624+715-1300 kg

= 39 kg.

Therefore, the weight of 13th student is 39 kg.

Question 24

The mean score of 25 observations is 80 and the mean score of another 55 observations is 60. Determine the mean score of the whole set of observations .

Solution 24

Mean score of 25 observations = 80

Total score of 25 observations = 80x25 = 2000

Mean score of 55 observations = 60

Total score of 55 observations = 60x55 =3300

Total no. of observations = 25+55 =80 observations

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped DataTotal score = 2000+3300 = 5300

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped DataMean score =R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 25

Arun scored 36 marks in English , 44 marks in hindi, 75 marks in mathematics and x marks in science . If he has secured an average of 50 marks , find the value of x.

Solution 25

Average marks of 4 subjects = 50

Total marks of 4 subjects = 50x4 = 200

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data36 + 44 + 75 + x = 200

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data 155  + x = 200

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data x = 200 - 155 = 45

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped DataThe value of x = 45

Question 26

A ship sails out to an island at the rate of 15 km/h and the sails back to the starting point at 10 km /h . find the average sailing speed for the whole journey .

Solution 26

Let the distance of mark from the staring point be x km.

Then , time taken by the ship reaching the marks=R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Time taken by the ship reaching the starting point from the marks =R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Total time taken =R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Total distance covered =x+x=2x km.


 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 27

There are 50 students in a class, of which 40 are boys . The average weight of the class is 44 kg and that of the girls is 40 kg . find the average weight of the boys.

Solution 27

Total number of students = 50

Total number of girls = 50-40 = 10

Average weight of the class = 44 kg

Total weight of 50 students= 44x 50 kg = 2200kg

Average weight of 10 girls = 40 kg

Total weight of 10 girls = 40x10 kg = 400 kg

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped DataTotal weight of 40 boys = 2200-400 kg =1800 kg

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Datathe average weight of the boys = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 28

The aggregate monthly expenditure of a family was Rs.18720 during the first 3 months, Rs.20340 during the next 4 months and Rs.21708 during the last 5 months of a year. If the total saving during the year be Rs.35340. Find the average monthly income of the family.

Solution 28

Total earnings of the year

= Rs. (3 × 18720 + 4 × 20340 + 5 ×21708 + 35340)

= Rs. (56160 + 81360 + 108540 + 35340)

= Rs. 281400

Number of months = 12

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 29

The average weekly payment to 75 workers in a factory is Rs.5680. The mean weekly payment to 25 of them is Rs.5400 and that of 30 others is Rs.5700. Find the mean weekly payment of the remaining workers.

Solution 29

Average weekly payment of 75 workers = Rs. 5680

Total weekly payment of 75 workers = Rs. (75 × 5680) = Rs. 426000

 

Mean weekly payment of 25 workers = Rs. 5400

Total weekly payment of 25 workers = Rs. (25 × 5400) = Rs. 135000

 

Mean weekly payment of 30 workers = Rs. 5700

Total weekly payment of 30 workers = Rs. (30 × 5700) = Rs. 171000

 

Number of remaining workers = 75 - 25 - 30 = 20

Therefore, Total weekly payment of remaining 20 workers

= Rs. (426000 - 135000 - 171000)

= Rs. 120000

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 30

The mean marks (out of 100) of boys and girls in an examination are 70 and 73 respectively. If the mean marks of all the students in that examination is 71, find the ratio of the number of boys to the number of girls.

Solution 30

Let the ratio of number of boys to the number of girls be x : 1.

Then,

Sum of marks of boys = 70x

Sum of marks of girls = 73 × 1 = 73

And, sum of marks of boys and girls = 71 × (x + 1)

70x + 73 = 71(x + 1)

70x + 73 = 71x + 71

x = 2

Hence, the ratio of number of boys to the number of girls is 2 : 1.

Question 31

The average monthly salary of 20 workers in an office is Rs.45900. If the manager's salary is added, the average salary becomes Rs.49200 per month. What's manager's monthly salary?

Solution 31

Mean monthly salary of 20 workers = Rs. 45900

Total monthly salary of 20 workers = Rs. (20 × 45900) = Rs. 918000

 

Mean monthly salary of 20 workers + manager = Rs. 49200

Total monthly salary of 20 workers + manager = Rs. (21 × 49200) = Rs. 1033200

 

Therefore, manager's monthly salary = Rs. (1033200 - 918000) = Rs. 115200

Chapter 18 - Mean, Median and Mode of Ungrouped Data Exercise Ex. 18C

Question 1(i)

Find the median of:

2,10, 9, 9, 5, 2, 3, 7, 11

Solution 1(i)

Arranging the data in accending order, we have

2,2,3, 5, 7, 9, 9, 10, 11

Here n = 9, which is odd

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

 

Question 1(ii)

Find the median of:

15, 6, 16, 8, 22, 21, 9, 18, 25

Solution 1(ii)

Arranging the data in ascending order , we have

6, 8, 9, 15, 16, 18, 21, 22, 25

Here n = 9, which is odd

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 1(iii)

Find the median of

20, 13, 18, 25, 6, 15, 21, 9, 16, 8, 22

Solution 1(iii)

Arranging data in ascending order:

6, 8, 9, 13, 15, 16, 18, 20, 21, 22, 25

Here n = 11 odd

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 1(iv)

Find the median of:

7, 4, 2, 5, 1, 4, 0, 10, 3, 8, 5, 9, 2

Solution 1(iv)

Arranging the data in ascending order , we have

0, 1, 2, 2, 3, 4, 4, 5, 5, 7, 8, 9, 10

Here n = 13, which is odd

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 2(iii)

Find the median of:

10, 75, 3, 15, 9, 47, 12, 48, 4, 81, 17, 27

Solution 2(iii)

Arranging the data in ascending order , we have

3, 4, 9, 10, 12, 15, 17, 27, 47, 48, 75, 81 Here n = 12, which is even

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 2(ii)

Find the median of:

72, 63, 29, 51, 35, 60, 55, 91, 85, 82

Solution 2(ii)

Arranging the data in ascending order , we have

29, 35, 51, 55, 60, 63, 72, 82, 85, 91

Here n = 10, which is even

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 2(i)

Find the median of:

17, 19, 32, 10, 22, 21, 9, 35

Solution 2(i)

Arranging the data in ascending order , we have

9, 10, 17, 19, 21, 22, 32, 35

Here n = 8, which is even

 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 3

The marks of 15 students in an examination are :

25,19,17,24,23,29,31,40,19,20,22,26,17,35,21

Find the median score.

Solution 3

Arranging the data in ascending order , we have

17, 17, 19, 19, 20, 21, 22, 23, 24, 25, 26, 29, 31, 35, 40

Here n = 15, which is odd

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Thus, the median score is 23.


Question 4

The heights (in cm) of 9 students of a class are

148, 144, 152, 155, 160, 147, 150, 149, 145.

Find the median height

Solution 4

Total number of students = n = 9 (odd)

Arranging heights (in cm) in ascending order, we have

144, 145, 147, 148, 149, 150, 152, 155, 160

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 5

The weights (in kg ) of 8 children are:

13.4, 10.6, 12.7, 17.2, 14.3, 15, 16.5, 9.8

Find the median weight.

Solution 5

Arranging the weights of 8 children in ascending order, we have

9.8, 10.6, 12.7, 13.4, 14.3, 15, 16.5, 17.2

Here , n= 8 , which is even

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 6

The ages (in years ) of 10 teachers in a school are:

32, 44, 53, 47, 37, 54, 34, 36, 40, 50

Fid the median age.

Solution 6

Arranging the ages of teachers in ascending order , we have

32, 34, 36, 37, 40, 44, 47, 50, 53, 54

Here, n =10, which is even

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 7

If 10, 13, 15, 18, x+1, x+3, 30, 32, 35, 41 are ten observations in an ascending order with median 24, find the value of x.

Solution 7

  The  ten observations in ascending order:

10, 13, 15, 18, x+1, x+3, 30, 32, 35, 41

Here, n =10, which is even

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 8

The following observations are arranged in ascending order:

26, 29, 42, 53, x, x + 2, 70, 75, 82, 93.

If the median is 65, find the value of x.

Solution 8

Total number of observations = n = 10 (even)

Median = 65

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data 

Question 9

The numbers 50, 42, 35, (2x + 10), (2x - 8), 12, 11, 8 have been written in a descending order. If their median is 25, find the value of x.

Solution 9

Total number of observations = n = 8 (even)

Median = 25

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data 

Question 10

Find the median of the data

46, 41, 77, 58, 35, 64, 87, 92, 33, 55, 90.

In the above data, if 41 and 55 are replaced by 61 and 75 respectively, what will be the new median?

Solution 10

Total number of observations = n = 11 (odd)

Arranging data in ascending order, we have

33, 35, 41, 46, 55, 58, 64, 77, 87, 90, 92

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Now, 41 and 55 are replaced by 61 and 75 respectively. 

Arranging new data in ascending order, we have

33, 35, 46, 58, 61, 64, 75, 77, 87, 90, 92

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Chapter 18 - Mean, Median and Mode of Ungrouped Data Exercise Ex. 18D

Question 1

Find the mode of the following items.

0, 6, 5, 1, 6, 4, 3, 0, 2, 6, 5, 6

Solution 1

Arrange the given data in ascending order we have

0, 0, 1, 2, 3, 4, 5, 5, 6, 6, 6, 6

Let us prepare the following table:

Observations(x)

0

1

2

3

4

5

6

Frequency

2

1

1

1

1

2

4

As 6 ocurs the maximum number of times i.e. 4, mode = 6

Question 2

Determine the mode of the following values of a variable.

23, 15, 25, 40, 27, 25, 22, 25, 20

Solution 2

Arranging the given data in ascending order , we have:

15, 20, 22, 23, 25, 25, 25, 27, 40

The frequency table of the data is :

Observations(x)

15

20

22

23

25

27

40

Frequency

1

1

1

1

3

1

1

As 25 ocurs the maximum number of times i.e. 3, mode = 25

Question 3

Calculate the mode of the following sizes of shoes by a shop on a particular day

5, 9, 8, 6, 9, 4, 3, 9, 1, 6, 3, 9, 7, 1, 2, 5, 9

Solution 3

Arranging the given data in ascending order , we have:

1, 1, 2, 3, 3, 4, 5, 5, 6, 6, 7, 8, 9, 9, 9, 9, 9,

The frequency table of the data is :

Observations(x)

1

2

3

4

5

6

7

8

9

Frequency

2

1

2

1

2

2

1

1

5

As 9, occurs the maximum number of times i.e. 5, mode = 9

Question 4

A cricket player scored the following runs in 12 one-day matches:

50, 30, 9, 32, 60, 50, 28, 50, 19, 50, 27, 35.

Find his modal score.

Solution 4

Arranging the given data in ascending order , we have:

9, 19, 27, 28, 30, 32, 35, 50, 50, 50, 50, 60

The frequency table of the data is :

Observations(x)

9

19

27

28

30

32

35

50

60

Frequency

1

1

1

1

1

1

1

4

1

As 50, ocurs the maximum number of times i.e. 4, mode = 50

Thus, the modal score of the cricket player is 50.

Question 5

If the mean of the data 3, 21, 25, 17, (x + 3), 19, (x - 4) is 18, find the value of x. Using this value of x, find the mode of the data.

Solution 5

Total number of observations = n = 7

Mean = 18

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Thus, data is as follows:

3, 21, 25, 17, 24, 19, 17

The most occurring value is 17.

Hence, the mode of the data is 17.

Question 6

The numbers 52, 53, 54, 54, (2x + 1), 55, 55, 56, 57 have been arranged in an ascending order and their median is 55. Find the value of x and hence find the mode of the given data.

Solution 6

Number of values = n = 9 (odd)

Numbers in ascending order:

52, 53, 54, 54, (2x + 1), 55, 55, 56, 57 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data 

Thus, we have

52, 53, 54, 54, 55, 55, 55, 56, 57

The most occurring number is 55.

Hence, the mode of the data is 55. 

Question 7

For what value of x is the mode of the data 24, 15, 40, 23, 27, 26, 22, 25, 20, x + 3 found 25? Using this value of x, find the median.

Solution 7

Mode of the data = 25

So, we should have the value 25 occurring maximum number of times in the given data.

That means, x + 3 = 25

x = 22

Thus, we have 24, 15, 40, 23, 27, 26, 22, 25, 20, 25.

Arranging data in ascending order, we have

15, 20, 22, 23, 24, 25, 25, 26, 27, 40

Number of observations = 10 (even)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 8

The numbers 42, 43, 44, 44, (2x + 3), 45, 45, 46, 47 have been arranged in an ascending order and their median is 45. Find the value of x. Hence, find the mode of the above data.

Solution 8

Total number of observations = n = 9 (odd)

Median = 45

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data 

Thus, we have

42, 43, 44, 44, 45, 45, 45, 46, 47

The most occurring value is 45.

Hence, the mode of the data is 45.

Chapter 18 - Mean, Median and Mode of Ungrouped Data Exercise Ex. 18B

Question 1

Obtain the mean of the following distribution:

Variable (xi)

4

6

8

10

12

Frequency (fi)

4

8

14

11

3

 

Solution 1

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 2

The following table shows the weights of 12 workers in a factory :

Weight (in Kg)

60

63

66

69

72

No of workers

4

3

2

2

1

Find the mean weight of the workers.

Solution 2

For calculating the mean , we prepare the following frequency table :

Weight (in kg)

(Xi)

No of workers

(fi)

fiXi

60

63

66

69

72

4

3

2

2

1

240

189

132

138

72

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data 

771

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

 

Question 3

The measurements (in mm) of the diameters of the heads of 50 screws are given below:

Diameter (in mm) (xi)

34

37

40

43

46

Number of screws (fi)

5

10

17

12

6

 

Calculate the mean diameter of the heads of the screws.

Solution 3

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 4

The following data give the number of boys of a particular age in a class of 40 students.

Age (in years)

15

16

17

18

19

20

Frequency (f)

3

8

9

11

6

3

Calculate the mean age of the students

Solution 4

For calculating the mean , we prepare the following frequency table :

Age (in years)

(Xi)

Frequency

(fi)

fiXi

15

16

17

18

19

20

3

8

9

11

6

3

45

128

153

198

114

60

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data 

698

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 5

Find the mean of the following frequency distribution :

Variable (xi)

10

30

50

70

89

Frequency(fi)

7

8

10

15

10

Solution 5

For calculating  the mean , we prepare  the following frequency table :

Variable

(Xi)

Frequency

(fi)

fiXi

10

30

50

70

89

7

8

10

15

10

70

240

500

1050

890

 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

  R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 6

Find the mean of daily wages of 40 workers in a factory as per data given below:

 

Daily wages (in Rs.) (xi)

250

300

350

400

450

Number of workers (fi)

8

11

6

10

5

 

Solution 6

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 7

If the mean of the following data is 20.2, find the value of p.

Variable (xi)

10

15

20

25

30

Frequency (fi)

6

8

p

10

6

 

Solution 7

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 8

If the mean of the following frequency distribution is 8, find the value of p.

X

3

5

7

9

11

13

F

6

8

15

p

8

4

Solution 8

We prepare  the following frequency table :

 

(Xi)

(fi)

fiXi

3

5

7

9

11

13

6

8

15

P

8

4

18

40

105

9P

88

52

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data 303 + 9p = 8(41+p)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data 303 + 9p= 328 + 8p

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data 9p - 8p = 328 -303

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data P=25

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data the value of P=25

Question 9

Find the missing frequency p for the following frequency distribution whose mean is 28.25.

X

15

20

25

30

35

40

F

8

7

p

14

15

6

Solution 9

We prepare the following frequency distribution table:

(Xi)

(fi)

fiXi

15

20

25

30

35

40

8

7

P

14

15

6

120

140

25p

420

525

240

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data 1445 + 25p = (28.25)(50+p)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data 1445 + 25p = 1412.50 + 28.25p

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data -28.25p + 25p = -1445 + 1412.50

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data -3.25p = -32.5

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data the value of p=10

Question 10

Find the value of p for the following frequency distribution whose mean is 16.6.

X

8

12

15

p

20

25

30

F

12

16

20

24

16

8

4

Solution 10

We prepare the following frequency distribution table:

(Xi)

(fi)

fiXi

8

12

15

P

20

25

30

12

16

20

24

16

8

4

96

192

300

24p

320

200

120

 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data 1228 + 24p = 1660

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data 24p = 1660-1228

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data 24p = 432

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data the value of p =18

Question 11

Find the missing frequencies in the following frequency distribution whose mean is 34.

x

10

20

30

40

50

60

Total

f

4

f1

8

f2

3

4

35

 

Solution 11

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 12

Find the missing frequencies in the following frequency distribution, whose mean is 50.

x

10

30

50

70

90

Total

f

17

f1

32

f2

19

120

Solution 12

Let f1  and f2 be the missing frequencies. 

We prepare the following frequency distribution table.

 

(Xi)

(fi)

fixi

10

30

50

70

90

17

f1

32

f2

19

170

30f1

1600

70f2

1710

Total

120

3480 + 30f+ 70f2

Here, 

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Thus, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data .......(1)

Also,

 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Substituting the value of f1 in equation 1, we have,

f2=52 - 28 = 24

Thus, the missing frequencies are f1 =28 and f2=24 respectively.

Question 13

Find the value of p, when the mean of the following distribution is 20.

x

15

17

19

20 + p

23

f

2

3

4

5p

6

 

Solution 13

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data

Question 14

The mean of the following distribution is 50.

x

10

30

50

70

90

f

17

5a + 3

32

7a - 11

19

 

Find the value of a and hence the frequencies of 30 and 70.

Solution 14

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 9 Mathematics Chapter - Mean Median And Mode Of Ungrouped Data