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Question
Construct a frequency distribution table for the following weights (in grams) of 35 mangoes, using the equal class intervals, one of them is 40 – 45 (45 not included).
30, 40, 45, 32, 43, 50, 55, 62, 70, 70, 61, 62, 53, 52, 50, 42, 35, 37, 53, 55, 65, 70, 73, 74, 45, 46, 58, 59, 60, 62, 74, 34, 35, 70, 68.
- How many classes are there in the frequency distribution table?
- Which weight group has the highest frequency?
Solution
| Class interval | Tally marks | Frequency |
| 30 – 35 | `bb|bb|bb|` | 3 |
| 35 – 40 | `bb|bb|bb|` | 3 |
| 40 – 45 | `bb|bb|bb|` | 3 |
| 45 – 50 | `bb|bb|bb|` | 3 |
| 50 – 55 | `\cancel(bb|bb|bb|bb|)` | 5 |
| 55 – 60 | `bb|bb|bb|bb|` | 4 |
| 60 – 65 | `\cancel(bb|bb|bb|bb|)` | 5 |
| 65 – 70 | `bb|bb|` | 2 |
| 70 – 75 | `\cancel(bb|bb|bb|bb|) bb|bb|` | 7 |
| Total | 35 |
- There are total number of 9 classes in the frequency distribution table.
- The weight group 70 – 75 has the highest frequency i.e. 7.
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Complete the Following Table.
| Classes (age) | Tally marks | Frequency (No. of students) |
| 12-13 | `cancel(bb|bb|bb|bb|)` | `square` |
| 13-14 | `cancel(bb|bb|bb|bb|)` `cancel(bb|bb|bb|bb|)` `bb|bb|bb|bb|` | `square` |
| 14-15 | `square` | `square` |
| 15-16 | `bb|bb|bb|bb|` | `square` |
| N = ∑f = 35 |
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The value of π up to 50 decimal place is
3.14159265358979323846264338327950288419716939937510
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( i )
| Class Interval | Frequency |
| 0 - 8 | 9 |
| 8 - 16 | 13 |
| 16 - 24 | 12 |
| 24 - 32 | 7 |
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( ii )
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| 41 - 50 | 10 |
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08 |
17 |
33 |
41 |
47 |
23 |
20 |
34 |
|
09 |
18 |
42 |
14 |
30 |
19 |
29 |
11 |
|
36 |
48 |
40 |
24 |
22 |
02 |
16 |
21 |
|
15 |
32 |
47 |
44 |
33 |
01 |
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| Class Interval | 20 - 24 | 25 29 | 30 - 34 | 35 - 39 | 40 - 44 | 45 - 49 |
| Frequency | 6 | 12 | 10 | 15 | 9 | 2 |
a. The true class limits of the fifth class.
b. The size of the second class.
c. The class boundaries of the fourth class.
d. The upper and lower limits of the sixth class.
e. The class mark of the third class.
Inclusive series is a continuous series
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Using the following frequency table.
| Marks (obtained out of 10) | 4 | 5 | 7 | 8 | 9 | 10 |
| Frequency | 5 | 10 | 8 | 6 | 12 | 9 |
10 marks the highest frequency.
Complete the following table:
| Weights (in kg.) |
Tally Marks | Frequency (Number of persons) |
| 40 – 50 | `\cancel(bb|bb|bb|bb|) \cancel(bb|bb|bb|bb|) bb|bb|` | |
| 50 – 60 | `\cancel(bb|bb|bb|bb|) \cancel(bb|bb|bb|bb|) bb|bb|bb|bb|` | |
| 60 – 70 | `\cancel(bb|bb|bb|bb|) bb|` | |
| 70 – 80 | `bb|bb|` | |
| 80 – 90 | `bb|` |
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