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

The following table gives the distribution of the lifetime of 400 neon lamps:

From the given table, we have the frequency distribution table as,

We have,
N

= 399

We know,

n = N 2 = 3992 = 199.5.

Here, the cumulative frequency just greater than 199.5 is 215 and the corresponding class is

3000 − 3500.

Therefore, the median class is

3000 − 3500.

Calculating the median.
The general formula for median is given as,
Median

= l + \frac{\frac{N}{2} - C . F .}{f} \times h

Where,
l = lower limit of median class

= 3000 .

C.F. = C.F. of previous class

= 130 .

f = frequency of median class

= 85 .

h = width of median class = upper limit - lower limit

\Rightarrow h = 3500 - 3000

\Rightarrow h = 500

Substitute all the values in median formula,

\Rightarrow Median = 3000 + (\frac{(199.5 - 130)}{85}) \times 500

\Rightarrow Medain = 3000 + \frac{69.5}{85} \times 500

\Rightarrow Medain = 3000 + 0.8176 \times 500

\Rightarrow Median = 3000 + 408.823529

\Rightarrow Medain = 3408.823529

Therefore, the median lifetime of a lamp = 3408.82 hours.
Hence, option (1) is correct.

The following table gives the distribution of the lifetime of 400 neon lamps:

Find the median life-time of a lamp.