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प्रश्न
The following are the marks (out of 100) of 60 students in mathematics.
16, 13, 5, 80, 86, 7, 51, 48, 24, 56, 70, 19, 61, 17, 16, 36, 34, 42, 34, 35, 72, 55, 75, 31, 52, 28, 72, 97, 74, 45, 62, 68, 86, 35, 85, 36, 81, 75, 55, 26, 95, 31, 7, 78, 92, 62, 52, 56, 15, 63, 25, 36, 54, 44, 47, 27, 72, 17, 4, 30.
Construct a grouped frequency distribution table with width 10 of each class starting from 0 – 9.
उत्तर
First, arranging the given data in ascending order.
4, 5, 7, 7, 13, 15, 16, 16, 17, 17, 19, 24, 25, 26, 27, 28, 30, 31, 31, 34, 34, 35, 35, 36, 36, 36, 42, 44, 45, 47, 48, 51, 52, 52, 54, 55, 55, 56, 56, 61, 62, 62, 63, 68, 70, 72, 72, 72, 74, 75, 75, 78, 80, 81, 85, 86, 86, 92, 95, 97.
We arrange the given data into groups like 0 – 9, 10 – 19, 20 – 29, ... The class width in each case is 10.
The frequency distribution of the given data is given below:
| Class interval | Tally marks | Frequency |
| 0 – 9 | `bb|bb|bb|bb|` | 4 |
| 10 – 19 | `\cancel(bb|bb|bb|bb|) bb|bb|` | 7 |
| 20 – 29 | `\cancel(bb|bb|bb|bb|)` | 5 |
| 30 – 39 | `\cancel(bb|bb|bb|bb|) \cancel(bb|bb|bb|bb|)` | 10 |
| 40 – 49 | `\cancel(bb|bb|bb|bb|)` | 5 |
| 50 – 59 | `\cancel(bb|bb|bb|bb|) bb|bb|bb|` | 8 |
| 60 – 69 | `\cancel(bb|bb|bb|bb|)` | 5 |
| 70 – 79 | `\cancel(bb|bb|bb|bb|) bb|bb|bb|` | 8 |
| 80 – 89 | `\cancel(bb|bb|bb|bb|)` | 5 |
| 90 – 99 | `bb|bb|bb|` | 3 |
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संबंधित प्रश्न
A study was conducted to find out the concentration of sulphur dioxide in the air in parts per million (ppm) of a certain city. The data obtained for 30 days is as follows:-
| 0.03 | 0.08 | 0.08 | 0.09 | 0.04 | 0.17 |
| 0.16 | 0.05 | 0.02 | 0.06 | 0.18 | 0.20 |
| 0.11 | 0.08 | 0.12 | 0.13 | 0.22 | 0.07 |
| 0.08 | 0.01 | 0.10 | 0.06 | 0.09 | 0.18 |
| 0.11 | 0.07 | 0.05 | 0.07 | 0.01 | 0.04 |
(i) Make a grouped frequency distribution table for this data with class intervals as 0.00 - 0.04, 0.04 - 0.08, and so on.
(ii) For how many days, was the concentration of sulphur dioxide more than 0.11 parts per million?
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?
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, 77, 82, 87, 92, 97 and 102
(iii) 12.5, 17.5, 22.5, 27.5, 32.5, 37.5, 42.5, 47.5
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.
Following data gives the number of children in 40 families:
1,2,6,5,1,5, 1,3,2,6,2,3,4,2,0,0,4,4,3,2,2,0,0,1,2,2,4,3, 2,1,0,5,1,2,4,3,4,1,6,2,2.
Represent it in the form of a frequency distribution.
The number of books in different shelves of a library are as follows:
30, 32, 28, 24, 20, 25, 38, 37, 40, 45, 16, 20
19, 24, 27, 30, 32, 34, 35, 42, 27, 28, 19, 34,
38, 39, 42, 29, 24, 27, 22, 29, 31, 19, 27, 25
28, 23, 24, 32, 34, 18, 27, 25, 37, 31, 24, 23,
43, 32, 28, 31, 24, 23, 26, 36, 32, 29, 28, 21.
Prepare a cumulative frequency distribution table using 45-49 as the last class interval.
Given below is a cumulative frequency distribution table showing the ages of people living in a locality:
| Ace in years | No. of persons |
| Above 108 | 0 |
| Above 96 | 1 |
| Above 84 | 3 |
| Above 72 | 5 |
| Above 60 | 20 |
| Above 48 | 158 |
| Above 36 | 427 |
| Above 24 | 809 |
| Above 12 | 1026 |
| Above 0 | 1124 |
Prepare a frequency distribution table
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
30 children were asked about the number of hours they watched TV programmes last week. The results are recorded as under:
| Number of hours | 0 – 5 | 5 – 10 | 10 – 15 | 15 – 20 |
| Frequency | 8 | 16 | 4 | 2 |
Can we say that the number of children who watched TV for 10 or more hours a week is 22? Justify your answer.
The following are the marks (out of 100) of 60 students in mathematics.
16, 13, 5, 80, 86, 7, 51, 48, 24, 56, 70, 19, 61, 17, 16, 36, 34, 42, 34, 35, 72, 55, 75, 31, 52, 28, 72, 97, 74, 45, 62, 68, 86, 35, 85, 36, 81, 75, 55, 26, 95, 31, 7, 78, 92, 62, 52, 56, 15, 63, 25, 36, 54, 44, 47, 27, 72, 17, 4, 30.
Construct a grouped frequency distribution table with width 10 of each class, in such a way that one of the classes is 10 – 20 (20 not included).
