RD SHARMA SOLUTION CHAPTER -22 Tabular Representation of Statistical Data| CLASS 9TH MATHEMATICS-EDUGROWN

Chapter 22 – Tabular Representation of Statistical Data Exercise Ex. 22.1

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4Why do we group data?Solution 4The 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.Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9The 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.

Question 10

Solution 10

Question 11The number of runs scored by a cricket player in 25 innings are as follows:

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) Rearrange these runs in ascending order.

(ii) Determine the player’s highest score.

(iii) How many times did the player not score a run?

(iv) How many centuries did he score?

(v) How many times did he score more than 50 runs?Solution 11The 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.Question 12

Solution 12

Question 13Write the class size and class limits in each of the following

(i) 104, 114, 124, 134, 144, 154, and 164

(ii) 47, 52, 57, 62, 67, 72, 82, 87, 92, 97 and 102

(iii) 12.5, 17.5, 22.5, 27.5, 32.5, 37.5, 42.5, 47.5Solution 13(i)

(ii)

(iii)

Question 14

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

Question 15

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

Question 16

The heights (in cm) of 30 students of class IX are given below:

155, 158,154, 158, 160, 148, 149, 150, 153, 159, 161, 148, 157, 153, 157, 162, 159, 151, 154, 156, 152, 156, 160, 152, 147, 155, 163, 155, 157, 153.

Prepare a frequency distribution table with 160-164 as one of the class intervals.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

Question 17

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

Question 18

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

Question 19

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

Question 20

The blood groups of 30 student of Class VIII are recoded as follows:

A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O,

A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O.

Represent this data in the form of a frequency distribution table. Which is the most common, and which is the rarest, blood group among these students?Solution 20Here 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.Question 21Three coins were tossed 30 times simultaneously. Each time the number of heads occurring was noted down as follows:
              0    1    2    2    1    2    3    1    3    0
              1    3    1    1    2    2    0    1    2    1
              3    0    0    1    1    2    3    2    2    0

Prepare a frequency distribution table for the data given above.   

Solution 21By 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

Question 22Thirty children were asked about the number of hours they watched TV programmes in the previous week. The results were found as follows:

     1    6    2      3    5    12      5    8      4     8
    10   3    4      12   2     8      15   1    17     6
     3    2    8      5    9      6      8    7    14    12

    (i)    Make a grouped frequency distribution table for this data, taking class width 5 and one of the class intervals as 5 – 10.
    (ii)    How many children watched television for 15 or more hours a week? 

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).

Question 23

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

Chapter 22 – Tabular Representation of Statistical Data Exercise Ex. 22.2

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4Following are the the ages of 360 patients getting medical treatment in a hospital on a day:

Age (in years):	10 – 20	20 – 30	30 – 40	40 – 50	50 – 60	60 – 70
No. of Patients:	90	50	60	80	50	30

Construct a cumulative frequency distribution.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

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8The following cumulative frequency distribution table shows the daily electricity consumption (in kW) of 40 factories in an industrial state:

Consumption (in KW)	No. of Factories
Below 240 Below 270 Below 300 Below 330 Below 360 Below 390 Below 420	1 4 8 24 33 38 40

(i) Represent this as a frequency distribution table.

(ii) Prepare a cumulative frequency table.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

Question 9

Solution 9