# The lengths of 40 leaves of a plant are measured correct to the nearest millimetre, 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.).

**Solution:**

Median Class is the class having Cumulative frequency (cf) just greater than n/2

Median = l + (n/2 - cf)/f × h

- Class size, h
- Number of observations, n
- Lower limit of median class, l
- Frequency of median class, f
- Cumulative frequency of class preceding median class, cf

From the table, it can be observed that n = 40 ⇒ n/2 = 20

Cumulative frequency (cf) just greater than 20 is 29, belonging to class 144.5 - 153.5

Therefore, median class = 144.5 - 153.5

Class size, h = 9

Lower limit of median class, l = 144.5 Frequency of median class, f = 12

Cumulative frequency of class preceding median class, cf = 17

Median = l + (n/2 - cf)/f × h

= 144.5 + (20 - 17)/12 × 9

= 144.5 + 3/12 × 9

= 144.5 + 9/4

= 144.5 +2.25

= 146.75

Therefore, median length of leaves is 146.75 mm.

**Video Solution:**

## The lengths of 40 leaves of a plant are measured correct to the nearest millimetre, and the data obtained is represented in the following table: Find the median length of the leaves.

### NCERT Solutions for Class 10 Maths - Chapter 14 Exercise 14.3 Question 4:

The lengths of 40 leaves of a plant are measured correct to the nearest millimetre, and the data obtained is represented in the following table: Find the median length of the leaves.

The median length of the leaves for a plant having 40 leaves is 146.75 mm.