Class 9 RD SHARMA Solutions Maths Chapter 22 - Tabular Representation of Statistical Data

Ex. 22.1

Ex. 22.2

22.26

22.27

Tabular Representation of Statistical Data Exercise Ex. 22.1

Solution 1

Solution 2

Solution 3

Solution 4

The data obtained in original form are called raw data. Raw data does not give any useful information and is rather confusing to mind. Data is grouped so that it becomes understandable and can be interpreted. We form groups according to various characteristics. After grouping the data, we are in a position to make calculations of certain values which will help us in describing and analysing the data.

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

The final marks in mathematics of 30 students are as follows:

53,61,48,60,78,68,55,100,67,90,75,88,77,37,84,58,60,48,62,56,44,58,52,64,98,59,70,39,50,60

(i)

Group	I(30-39)	II(40-49)	III(50-59)	IV(60-69)	V(70-79)	VI(80-89)	VII(90-99)	VIII(100-109)
Observations	37, 39	44, 48, 48	50, 52, 53, 55, 56, 58, 58, 59	60, 60, 60, 61, 62, 64, 67, 68	70, 75, 77, 78	84, 88	90, 98	100

(ii) Highest score = 100

(iii) Lowest score = 37

(iv) Range = 100 - 37 = 63

(v) If 40 is the pass mark, 2 students have failed.

(vi) 8 students have scored 75 or more.

(vii) Observations 51, 54, 57 between 50 and 60 have not actually appeared.

(viii) 5 students have scored less than 50.

Solution 10

Solution 11

The numbers of runs scored by a player in 25 innings:

26, 35, 94, 48, 82, 105, 53, 0, 39, 42, 71, 0, 64, 15, 34, 67, 0, 42, 124, 84, 54, 48, 139, 64, 47.

(i) Runs in ascending order:- 0,0,0,15,26,34,35,39,42,42,47,48,48,53,54,64,64,67,71,82,84,94,105,124,139

(ii) The highest score = 139

(iii) The player did not score any run 3 times.

(iv) He scored 3 centuries.

(v) He scored more than 50 runs 12 times.

Solution 12

Solution 13

(i)

(ii)

(iii)

Solution 14

Number of children	Tally marks	Number of families
0		5
1	ll	7
2	ll	12
3		5
4	l	6
5	lll	3
6	lll	3

Solution 15

Marks	Tally marks	Frequency
20 - 30	l	1
30 - 40	lll	3
40 - 50		5
50 - 60	lll	8
60 - 70	lll	8
70 - 80	llll	9
80 - 90	llll	4
90 - 100	ll	2
		Total = 40

Solution 16

Heights (in cm)	Tally marks	Frequency
145 - 149	llll	4
150 - 154	llll	9
155 - 159	ll	12
160 - 164		5
		Total = 30

Solution 17

Height (in cm)	Tally marks	Frequency
800 - 810	lll	3
810 - 820	ll	2
820 - 830	l	1
830 - 840	lll	8
840 - 850		5
850 - 860	l	1
860 - 870	lll	3
870 - 880	l	1
880 - 890	l	1
890 - 900		5
		Total = 30

Solution 18

Maximum temperature (in degree Celsius)	Tally marks	Frequency
20.0 - 21.0	l	6
21.0 - 22.0		5
22.0 - 23.0	llll	9
23.0 - 24.0		5
24.0 - 25.0	lll	3
25.0 - 26.0	ll	2
		Total = 30

Solution 19

Monthly wages (in rupees)	Tally marks	Frequency
210 - 230	llll	4
230 - 250	llll	4
250 - 270		5
270 - 290	lll	3
290 - 310	ll	7
310 - 330		5
		Total = 28

Solution 20

Here 9 students have blood groups A, 6 as B, 3 as AB and 12 as O.
So, the table representing the data is as follows:

Blood group	Number of students
A	9
B	6
AB	3
O	12
Total	30

As 12 students have the blood group O and 3 have their blood group as AB. Clearly, the most common blood group among these students is O and the rarest blood group among these students is AB.

Solution 21

By observing the data given above following frequency distribution table can be constructed

Number of heads	Number of times (frequency)
0	6
1	10
2	9
3	5
Total	30

Solution 22

(i) Class intervals will be 0 - 5, 5 - 10, 10 -15.....
The grouped frequency distribution table is as follows:

Hours	Number of children
0 - 5	10
5 - 10	13
10 - 15	5
15 - 20	2
Total	30

(ii) The number of children, who watched TV for 15 or more hours a week
is 2 (i.e. number of children in class interval 15 - 20).

Solution 23

Since first class interval is -19.9 to -15

Frequency distribution with lower limit included and upper limit excluded is:

Temperature	Tally marks	Frequency
-19.9 to -15	ll	2
-15 to -10.1	ll	7
-10.1 to -5.2		5
-5.2 to -0.3	llll	4
-0.3 to 4.6	ll	17
Total		35

Tabular Representation of Statistical Data Exercise Ex. 22.2

Solution 1

Solution 2

Solution 3

Solution 4

Age (in years):	No. of patients	Age (in years)	Cumulative frequency
10 - 20	90	Less than 20	90
20 - 30	50	Less than 30	140
30 - 40	60	Less than 40	200
40 - 50	80	Less than 50	280
50 - 60	50	Less than 60	330
60 - 70	30	Less than 70	360
	N = 360

Solution 5

Solution 6

Solution 7

Solution 8

(i)

Consumption (in kW)	No. of Factories	Class interval	Frequency
Below 240	1	0 - 240	1
Below 270	4	240 - 270	4 - 1 = 3
Below 300	8	270 - 300	8 - 4 = 4
Below 330	24	300 - 330	24 - 8 = 16
Below 360	33	330 - 360	33 - 24 = 9
Below 390	38	360 - 390	38 - 33 = 5
Below 420	40	390 - 420	40 - 38 = 2

(ii)

Class interval	Frequency	Consumption (in kW)	No. of factories
0 - 240	1	More than 0	40
240 - 270	3	More than 270	40 - 1 = 39
270 - 300	4	More than 270	39 - 3 = 36
300 - 330	16	More than 300	36 - 4 = 32
330 - 360	9	More than 330	32 - 16 = 16
360 - 390	5	More than 360	16 - 9 = 7
390 - 420	2	More than 390	7 - 5 = 2
		More than 420	2 - 2 = 0
	N = 40

Solution 9

Tabular Representation of Statistical Data Exercise 22.26

Solution 1

When observations are large, it may not be easy to find the frequencies by simple counting.

So, we make use of tally marks.

Thus, Tally marks are used to find frequency.

Hence, correct option is (c).

Solution 2

The difference between the highest and lowest value of observations is called 'Range' of observations.

Hence, correct option is (c).

Solution 3

The difference between the upper class limit and the lower class limit is called class size.

Hence, correct option is (b).

Solution 4

Since, 10 - 20, 20 - 30 are Exclusive Class Intervals, the upper limit of a class is not included in the class.

Thus, 20, will be taken in the class 20 - 30.

Hence, correct option is (b).

Solution 5

$begin mathsize 12px style Let space the space lower space limit space be space straight x. Class space interval space equals space 4 rightwards double arrow Upper space limit space equals space straight x space plus space 4 Now comma space mid minus value space of space straight a space class space equals space fraction numerator straight x space plus space 4 space plus space straight x over denominator 2 end fraction equals straight x space plus space 2 space equals space 15 space left parenthesis given right parenthesis rightwards double arrow straight x space equals space 13 space equals space lower space limit Hence comma space correct space option space is space left parenthesis straight c right parenthesis. end style$

Solution 6

$begin mathsize 12px style Let space the space lower space limit space of space straight a space class space equals space straight x Class space size space equals space 10 rightwards double arrow Upper space limit space equals space straight x space plus space 10 Now comma space mid minus value space equals space fraction numerator straight x space plus space 10 space plus space straight x over denominator 2 end fraction equals straight x space plus space 5 space equals space 42 space left parenthesis given right parenthesis rightwards double arrow straight x space equals space 37 space equals space lower space limit rightwards double arrow straight x space plus space 10 space equals space 47 space equals space upper space limit Thus comma space upper space and space lower space limits space are space 47 comma space 37. Hence comma space correct space option space is space left parenthesis straight a right parenthesis. space end style$

Tabular Representation of Statistical Data Exercise 22.27

Solution 7

The number of times a particular item occurs in a given data is called its Frequency.

Hence, correct option is (b).

Solution 8

Number of classes = 9

Lower limit of the lowest class = 10.6

Width of each class = 2.5

So, Upper limit of the lowest class = 10.6 + 2.5 = 13.1

Now, Upper limit of the lowest class + Width of each class = Upper limit of the next class

Thus, we have

Upper limit of the lowest class + 8 × width of each class = Upper limit of the highest (9^th) class

Upper limit of the highest (9^th) class = 13.1 + 8 × 2.5 = 33.1

Hence, correct option is (b).

Solution 9

Range of observations = Highest observation - Lowest observation

= 95 - 62

= 33

Hence, correct option is (d).

Solution 10

Tally are usually marked in a bunch of 5: 4 in a vertical line and one is placed diagonally.

Hence, correct option is (c).

Solution 11

$begin mathsize 12px style Let space the space class space size space equals space straight S Lower space limit space space equals space straight l rightwards double arrow Upper space limit space equals space straight l space plus space straight S Now comma space mid minus point space equals space fraction numerator straight l space plus space straight l space plus space straight S over denominator 2 end fraction space equals space straight m space space left parenthesis given right parenthesis rightwards double arrow straight S space equals space 2 straight m space minus space 2 straight l Then comma space Upper space limit space equals space straight l space plus space straight S space equals space straight l space plus space 2 straight m space minus space 2 straight l space equals space 2 straight m space minus space straight l Hence comma space correct space option space is space left parenthesis straight c right parenthesis. end style$

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Class 9 RD SHARMA Solutions Maths Chapter 22 - Tabular Representation of Statistical Data

Tabular Representation of Statistical Data Exercise Ex. 22.1

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14

Solution 15

Solution 16

Solution 17

Solution 18

Solution 19

Solution 20

Solution 21

Solution 22

Solution 23

Tabular Representation of Statistical Data Exercise Ex. 22.2

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Tabular Representation of Statistical Data Exercise 22.26

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Tabular Representation of Statistical Data Exercise 22.27

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

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