Class 9 MAHARASHTRA STATE TEXTBOOK BUREAU Solutions Maths Chapter 7 - Statistics

Sub-divided bar diagram:

Percentage bar diagram:

Information of attendance of every student collected by visiting every class in a school is a primary data. 

The information of heights of students was gathered from school records and sent to the head office, as it was to be sent urgently is a secondary data.

In the village Nandpur, the information collected from every house regarding students not attending school is a primary data.

For science project, information of trees gathered by visiting a forest is a primary data.

For the class interval 20 - 25

Lower class limit is 20

Upper class limit is 25

Class mark

= 37.5

∴ The class-mark of the class 35-40 is 37.5. 

Let the upper limit be x and lower limit be y.

∴ x + y = 20 … (I)

Class width = 6 … (Given)

∴ y - x = 6 … (II)

Adding equations (I) and (II), we get

2x = 26

∴ x = 13

Substituting this value of x in (I), we get

13 + y = 20

∴ y = 20 - 13

∴ y = 7

∴ The class is 7 - 13.

Let frequency of the class 14 - 15 be x.

∴ 5 + 14 + x + 4 = 35

∴ 23 + x = 35

∴ x = 35 - 23

∴ x = 12

Frequency distribution table is as follows:

Let the lower class limit and upper class limit of the class mark 5 be x and y respectively.

∴ x + y = 10 … (I)

Now, class width = 15 - 5 = 10

But, class width = Upper class limit - Lower class limit

∴ y - x = 10 … (II)

Adding equations (I) and (II), we get

 x + y = 10

-x + y = 10

∴ 2y = 20

∴ y = 10

Substituting this value of y in equation (I)

∴ x + 10 = 10

∴ x = 0

∴ The class with class-mark 5 is 0 - 10.

So, the next classes will be 10 - 20, 20 - 30, and so on.

∴ The frequency table taking inclusive and exclusive classes is given as:

Let the lower class limit and upper class limit of the class mark 22 be x and y respectively.

∴ x + y = 44 … (I)

Now, class width = 24 - 22 = 2

But, class width = Upper class limit - Lower class limit

∴ y - x = 2 … (II)

Adding equations (I) and (II), we get

 x + y = 44

-x + y = 2

∴ 2y = 46

∴ y = 23

Substituting this value of y in equation (I)

∴ x + 23 = 44

∴ x = 21

∴ The class with class-mark 5 is 21 - 23.

So, the next classes will be 23 - 25, 25 - 27, and so on.

∴ The frequency table taking inclusive and exclusive classes is given as:

The grouped frequency distribution table is as follows: 

(I)

 (ii)

Number of people who donated rupees 350 or more = 4 + 4 + 2 + 1 = 11

(i) 38 students obtained marks 40 or above 40.

(ii) 3 students obtained marks 90 or above 90.

(iii) 19 students obtained marks 60 or above 60.

(iv) Cumulative frequency of equal to or more than type of the class 0 - 10 is 62.

(i) 24 students obtained less than 40 marks.

(ii) 3 students obtained less than 10 marks.

(iii) 43 students obtained less than 60 marks.

(iv) Cumulative frequency of the class 50 - 60 is 43.

= 7

So, the mean of yield per acre is 7 quintals. 

Arranging the given data in ascending order:

59, 68, 70, 74, 75, 75, 80

Here, number of observations(n) = 7, which is odd

∴ Median is the middle most observation.

Here, 4^th number is at the middle position, which is = 74

∴ The median of the given data is 74.

Arranging the given data in ascending order:

60, 90, 95, 99, 100, 100, 100

Here, the observation repeated maximum number of times is 100.

∴ The mode of the given data is 100.

= Rs. 4900

∴ The mean of monthly salary is Rs. 4900.

Arranging the given data in ascending order:

50, 60, 65, 70, 70, 80 85, 90, 95, 95

∴ Number of observations (n) = 10, which is even

∴ Median is the average of the middle two observations

Here, 5^th and 6^th numbers are in the middle position

∴ The median of the weights of tomatoes is 75 grams.

(i)

Given observations are: 5, 4, 0, 2, 2, 4, 4, 3, 3.

Total number of observations = 9

= 3

∴ The mean of the given data is 3.

(ii)

Arranging the given data in ascending order:

0, 2, 2, 3, 3, 4, 4, 4, 5

∴ Number of observations(n) = 9, which is odd

∴ Median is the middle most observation

Here, the 5^th number is at the middle position, which is 3.

∴ The median of the given data is 3.

(iii)

Arranging the given data in ascending order:

0, 2, 2, 3, 3, 4, 4, 4, 5

Here, the observation repeated maximum number of times is 4.

∴ The mode of the given data is 4.

Here, mean = 80, number of observations = 50

∴ The sum of all observations = Mean × Total number of observations

∴ The sum of 50 observations = 80 × 50 = 4000

One of the observation was 19 and it was by mistake recorded as 91.

∴ Sum of observations after correction = sum of 50 observations + correct observation - incorrect observation

= 4000 + 19 - 91

= 3928

∴ Corrected mean

= 78.56

∴ The corrected mean is 78.56.

Arranging the given data in ascending order:

2, 3, 5, 9, x + 1, x + 3, 14, 16, 19, 20.

∴ Number of observations (n) = 10, which is even

∴ Median is the average of middle two observations.

Here, the 5^th and 6^th numbers are in the middle position.

∴ 22 = 2x + 4

∴ 22 - 4 = 2x

∴ 18 = 2x

∴ x = 9

∴ The sum of all observations = Mean × Total number of observations

Since, the mean of 35 observations is given as 20.

∴ Sum of 35 observations = 20 × 35 = 700 … (I)

As the mean of first 18 observations is given as 15

∴ Sum of first 18 observations = 15 × 18 = 270  … (II)

Also, since the mean of last 18 observations is 25

∴ Sum of last 18 observations = 25 × 18 = 450  … (III)

∴ 18^th observation = (Sum of first 18 observations + Sum of last 18 observations) - (Sum of 35 observations)

= (270 + 450) - (700) … [From (I), (II) and (III)]

= 720 - 700

= 20

∴ The 18^th observation is 20.

∴ The sum of all observations = Mean × Total number of observations

Since, the mean of 5 observations is 50.

∴ Sum of 5 observations = 50 × 5 = 250 … (I)

One observation was removed and mean of remaining data is 45.

Total number of observations after removing one observation = 5 - 1 = 4

Now, mean of 4 observations is 45.

∴ Sum of 4 observations = 45 × 4 = 180  … (II)

∴ Observation which was removed

 = Sum of 5 observations - Sum of 4 observations

 = 250 - 180  … [From (I) and (II)]

 = 70

∴ The observation which was removed is 70.

Total number of students = 40 and Number of boys =15

∴ Number of girls = 40 - 15 = 25

The mean of marks obtained by 15 boys is given as 33.

∴ Sum of the marks obtained by boys = 33 × 15 = 495  … (I)

The mean of marks obtained by 25 girls is given as 35

∴ Sum of the marks obtained by girls = 35 × 25 = 875  … (II)

Sum of the marks obtained by boys and girls

= 495 + 875  … [From (I) and (II)]

= 1370

∴ Mean of all the students

= 34.25

∴ The mean of all the students in the class is 34.25.

Arranging given data in ascending order:

35, 35, 37, 37, 37, 37, 40, 42, 42, 43

∴ The observation repeated maximum number of times is 37.

∴ Mode of the given data is 37 kg.

Here, the maximum frequency is 25.

Since, mode = observation having maximum frequency

∴ The mode of the given data is 2.

Here, the maximum frequency is 9.

Since, mode = observations having maximum frequency

As the two observations has this maximum frequency.

∴ Mode = 35 and 37

(C)

To get information regarding plantation of soyabean done by each farmer from the village Talathi is not primary. 

(B)

Upper class limit of the class 25 - 35 is 35.

(D)

= 30

Observation 10 must be included in the class 10 - 20.

(A)

Here,  is the mean of the observations are x₁, x₂, x₃, …, x_n

Since,  is the mean of the observations are y₁, y₂, y₃, …, y_n

Similarly,  

(D)

5^th number = Sum of five numbers - Sum of four numbers

= (5 × 50) - (4 × 46)

= 250 - 184

= 66

(B)

New sum of the observations = 100×40 - 30 + 70 = 4040

= 40.4

(A)

Observation repeated maximum number of times is 15.

∴ Mode = 15

(C)

Arranging the given observations in ascending order:

5, 7, 7, 9, 10, 10

Number of observations = 6, which is even

(C)

Cumulative frequency of less than type for the class 30 - 40 is 7+3+13+12 = 35

∴ The sum of all observations = Mean × Total number of observations

The mean salary of 20 workers is Rs. 10,250.

∴ Sum of the salaries of 20 workers

 = 20 × 10,250

 = Rs. 2,05,000  … (I)

If the superintendent's salary is added, then mean increases by 750.

∴ new mean = 10,250 + 750 = 11,000

Total number of people after adding superintendent = 20 + 1 = 21

∴ Sum of the salaries including the superintendent's salary

 = 21 × 11,000

 = Rs. 2,31,000  … (II)

∴ Superintendent's salary = sum of the salaries including superintendent's salary - sum of salaries of 20 workers

 = 2,31,00 - 2,05,000  … [From (I) and (II)]

 = Rs. 26,000

∴ The salary of the office superintendent is Rs. 26,000.

∴ The sum of all observations = Mean × Total number of observations mean of nine numbers is 77

∴ sum of 9 numbers = 11 × 9 = 693 … (I)

If one more number is added, then mean increases by 5

∴ Mean of 10 numbers = 77 + 5 = 82

∴ sum of the 10 numbers = 82 × 10 = 820  … (II)

∴ Number added = sum of the 10 numbers - sum of the 9 numbers

 = 820 - 693  … [From (I) and (II)]

 = 127

∴ The number added in the data is 127.

(i)

Number of days for which the maximum temperature was less than 34°C

= 8 + 8 + 8 = 24

(ii)

Number of days for which the maximum temperature was 34°C or more than 34°C

= 5 + 1 = 6

∴ 20.2 (30 + p) = 610 + 20p

∴ 606 + 20.2p = 610 + 20p

∴ 20.2p - 20p = 610 - 606

∴ 0.2p = 4

∴ p = 2

(i) 66 students have scored marks less than 80.

(ii) 14 students have scored marks less than 40.

(iii) 45 students have scored marks less than 60.

(i) 11 students have scored marks 70 or more than 70.

(ii) 68 students have scored marks 30 or more than 30.

(i)

Arranging the given data in ascending order:

45, 47, 50, 52, x, JC+2, 60, 62, 63, 74.

∴ Number of observations (n) = 10, which is even

∴ Median will be the average of middle two observations.

Here, the 5^th and 6^th numbers are in the middle position.

∴ 106 = 2x + 2

∴ 106 - 2 = 2x

∴ 104 = 2x

∴ x = 52

∴ The given data becomes:

45, 47, 50, 52, 52, 54, 60, 62, 63, 74.

(ii)

= 55.9

∴ The mean of the given data is 55.9.

(iii)

Arranging the given data in ascending order:

45, 47, 50, 52, 52, 54, 60, 62, 63, 74

∴ The observation repeated maximum number of times = 52

∴ The mode of the given data is 52.