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Question
In the following data, find the values of p and q. Also, find the median class and modal class.
| Class | Frequency (f) | Cumulative frequency (cf) |
| 100 – 200 | 11 | 11 |
| 200 – 300 | 12 | p |
| 300 – 400 | 10 | 33 |
| 400- 500 | Q | 46 |
| 500 – 600 | 20 | 66 |
| 600 – 700 | 14 | 80 |
Solution
Here, 𝑝=11+12=23
And 33+𝑞=46
⟹ 𝑞=46−33
= 13
Thus, p is 23 and q is 13.
Now,
Here the maximum class frequency is 20, and the class corresponding to this frequency is 500-600.
So, the modal class is 500-600.
Also, Σ 𝑓=𝑁= 80
⟹` N/2 = 40.`
The cumulative frequency just greater than 40 is 46, and the corresponding class is 400-500.
Thus, the median class is 400-500.
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