RD SHARMA Solutions for Class 9 Maths Chapter 22 - Tabular Representation of Statistical Data
Chapter 22 - Tabular Representation of Statistical Data Exercise 22.26
Question 1
Tally marks are used to find
(a) class intervals
(b) range
(c) frequency
(d) upper limits
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).
Question 2
The difference between the highest and lowest values of the observations is called
(a) frequesncy
(b) mean
(c) range
(d) class-intervals
Solution 2
The difference between the highest and lowest value of observations is called 'Range' of observations.
Hence, correct option is (c).
Question 3
The difference between the upper and the lower class limits is called
(a) mid-points
(b) class size
(c) frequency
(d) mean
Solution 3
The difference between the upper class limit and the lower class limit is called class size.
Hence, correct option is (b).
Question 4
In the class intervals 10 - 20, 20 - 30, 20 is taken in
(a) the interval 10 - 20
(b) the interval 20 - 30
(c) both intervals 10 - 20, 20 - 30
(d) none of the intervals
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).
Question 5
In a frequency distribution, the mid-value of a class is 15 and the class intervals is 4. The lower limit of the class is
(a) 10
(b) 12
(c) 13
(d) 14
Solution 5
Question 6
The mid-value of a class interval is 42. If the class size is 10, then the upper and lower limits of the class are:
(a) 47 and 37
(b) 37 and 47
(c) 37.5 and 47.5
(d) 47.5 and 37.5
Solution 6
Chapter 22 - Tabular Representation of Statistical Data Exercise 22.27
Question 1
The number of times a particular item occurs in a given data is called its
(a) variation
(b) frequency
(c) cumulative frequency
(d) class-size
Solution 1
The number of times a particular item occurs in a given data is called its Frequency.
Hence, correct option is (b).
Question 2
The width of each of nine classes in a frequency distribution is 2.5 and the lower class boundary of the lowest class 10.6. Then the upper class boundary of the highest class is
(a) 35.6
(b) 33.1
(c) 30.6
(d) 28.1
Solution 2
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 (9th) class
Upper limit of the highest (9th) class = 13.1 + 8 × 2.5 = 33.1
Hence, correct option is (b).
Question 3
The following marks were obtained by the students in a test:
81, 72, 90, 90, 86, 85, 92, 70, 71, 83, 89, 95, 85, 79, 62
The range of the marks is
(a) 9
(b) 17
(c) 27
(d) 33
Solution 3
Range of observations = Highest observation - Lowest observation
= 95 - 62
= 33
Hence, correct option is (d).
Question 4
Tally are usually marked in a bunch of
(a) 3
(b) 4
(c) 5
(d) 6
Solution 4
Tally are usually marked in a bunch of 5: 4 in a vertical line and one is placed diagonally.
Hence, correct option is (c).
Question 5
Let l be the lower class limit of a class-interval in a frequency distribution and m be the mid-point of the class. Then, the upper class limit of the class is
Solution 5
Chapter 22 - Tabular Representation of Statistical Data Exercise Ex. 22.1
Question 1
Solution 1
Question 2
Solution 2
Question 3
Solution 3
Question 4
Why do we group data?
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.
Question 5
Solution 5
Question 6
Solution 6
Question 7
Solution 7
Question 8
Solution 8
Question 9
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)
(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.
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 11
The 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?
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 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.
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 13
Write 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, 47.5
(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, 47.5
Solution 13
(i)
(ii)
(iii)
(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 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:
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 21
Three 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.
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 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 |
Question 22
Thirty 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?
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:
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 4
Following are the the ages of 360 patients getting medical treatment in a hospital on a day:
Construct a cumulative frequency distribution.
| 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 8
The following cumulative frequency distribution table shows the daily electricity consumption (in kW) of 40 factories in an industrial state:
(i) Represent this as a frequency distribution table.
(ii) Prepare a cumulative frequency table.
| 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
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