Find the median length of the leaves.

(Hint: The data needs to be converted to continuous classes for finding the median, since the formula assumes continuous classes. The classes then change to 117.5 – 126.5, 126.5 – 135.5, . . ., 171.5 – 180.5.)

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The given data does not have continuous class intervals. It can be observed that the difference between two class intervals is 1. Therefore, 1/2 = 0.5 has to be added and subtracted to upper class limits and lower-class limits respectively.

Continuous class intervals with respective cumulative frequencies he represented follows.

From the table, it can be observed that the cumulative frequency just greater than n/2 (i.e. 40/2 = 20) is 29, belonging to class interval 144.5 – 153.5.

Median class = 144.5 – 153.5

Lower Limit (l) of median class = 144.5 and class size (h) = 9

Frequency (f) of median class 12

Cumulative frequency (cf) of class preceding median class = 17

Median = l + (n/2 – cf)/f) × h = 144.5 + ((20 – 17)/12) × 9 = 144.5 + 2.25 = 146.75

Therefore, median length of leaves is 146.75mm.

See this explanation video for better understanding✌😃