# The following table gives the distribution of the life time of 400 neon lamps:

Find the median lifetime of a lamp.

**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

From the table, it can be observed that n = 400 ⇒ n/2 = 200

Cumulative frequency (cf) just greater than 200 is 216, belonging to class 3000 - 3500.

Therefore, median class = 3000 - 3500

Class size, h = 500

Lower limit of median class, l = 3000

Frequency of median class, f = 86

Cumulative frequency of class preceding median class, cf = 130

Median = l + [(n/2 - cf)/f] × h

= 3000 + [(200 - 130)/86] × 500

= 3000 + (70 × 500)/86

= 3000 + 17500/43

= 3000 + 406.98

= 3406.98

Therefore, median lifetime of lamps is 3406.98 hours.

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

**Video Solution:**

## The following table gives the distribution of the life time of 400 neon lamps: Find the median lifetime of a lamp.

NCERT Solutions for Class 10 Maths Chapter 14 Exercise 14.3 Question 5

**Summary:**

The median lifetime of a lamp, given the distribution of the lifetime of 400 neon lamps is 3406.98 hours.

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