# 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:**

We know that,

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

Let's construct a continuous class data.

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.

**☛ Check: **NCERT Solutions for Class 10 Maths Chapter 14

**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

**Summary:**

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

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