# 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.

**☛ Related Questions:**

- The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median, mean and mode of the data and compare them.
- If the median of the distribution given below is 28.5, find the values of x and y.
- A life insurance agent found the following data for distribution of ages of 100 policy holders. Calculate the median age, if policies are given only to persons having age 18 years onwards but less than 60 year.
- 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.).

visual curriculum