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Question
Find the mode of the following frequency distribution:
| Class: | 20 – 30 | 30 – 40 | 40 – 50 | 50 – 60 | 60 – 70 |
| Frequency: | 25 | 30 | 45 | 42 | 35 |
Solution
Since, class 40 – 50 have highest frequency.
So, modal class is 40 – 50.
Lower limit (l) of modal class = 40
Class size (h) = 10
Frequency of modal class (f1) = 45
Frequency of class proceeding to modal class (f0) = 30
Frequency of class succeeding to modal class (f2) = 42
Mode = `l + ((f_1 - f_0)/(2f_1 - f_0 - f_2)) xx h`
= `40 + ((45 - 30)/(90 - 30 - 42)) xx 10`
= `40 + 150/18`
= `(720 + 150)/18`
= `870/18`
= 48.33
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