The mean life of a sample of 60 bulbs was 650 hours and the standard deviation was 8 hours. A second sample of 80 bulbs has a mean life of 660 hours and standard deviation 7 hours. Find the overall standard deviation.

Given: The mean life of a sample of 60 bulbs was 650 hours and the standard deviation was 8 hours. A second sample of 80 bulbs has a mean life of 660 hours and standard deviation 7 hours

To find: the overall standard deviation

As per given criteria,

In first set of samples,

Number of sample bulbs, n₁=60

Standard deviation, s₁=8hrs

Mean life,

And in second set of samples,

Number of sample bulbs, n₂=80

Standard deviation, s₂=7hrs

Mean life,

We know the standard deviation for combined two series is

Substituting the corresponding values, we get

Or, σ=8.9

Hence the standard deviation of the set obtained by combining the given two sets is 8.9