Two sets each of 20 observations, have the same standard derivation 5. The first set has a mean 17 and the second a mean 22. Determine the standard deviation of the set obtained by combining the given two sets.

Given: Two sets each of 20 observations, have the same standard derivation 5. The first set has a mean 17 and the second a mean 22.

To show: the standard deviation of the set obtained by combining the given two sets

As per given criteria,

For first set

Number of observations, n₁=20

Standard deviation, s₁=5

And mean,

For second set

Number of observations, n₂=20

Standard deviation, s₂=5

And mean,

We know the standard deviation for combined two series is

Substituting the corresponding values, we get

Or, σ=5.59

Hence the standard deviation of the set obtained by combining the given two sets is 5.59