Question

In a certain company, every worker received a $50-per-week raise. How does this affect the mean salary and the standard deviation of the salaries?

Answer 1

The mean salary increases by $50.

The standard deviation remains the same.

Explanation:

Since the mean salary is the average of all salaries, and every work recieved the same $50 raise, the mean salary increases by $50.

As for the standard deviation, it measures the dispersion of all values within a data set from the mean. Since the mean and each value on the set all increased by $50, the difference between them remains the same:

`x_i-M = (X_i+50)-(M+50)`

Therefore, the standard deviation remains the same.