The lengths of 40 leaves of a plant are measured correct to the nearest millimeter, and the data obtained is represented in the following table :

Question

The lengths of 40 leaves of a plant are measured correct to the nearest millimeter, and the data obtained is represented in the following table :

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.)

Philoid · Accepted Answer

We’ll convert this inclusive data into exclusive data type.

For median:

We have, total frequency, N = 40

N/2 = 40/2 = 20

Observe, cf = 29 is just greater than 20.

Thus, median class = 144.5-153.5

Median is given by

Where,

L = Lower class limit of median class = 144.5

N/2 = 20

cf = cumulative frequency of the class preceding median class = 17

f = frequency of the median class = 12

h = class interval of the median class = 9

Substituting these values in the formula of median, we get

⇒

⇒ Median = 144.5 + 9/4

⇒ Median = 144.5 + 2.25

⇒ Median = 146.75

Thus, the median is 146.75 mm.