Mean, Quartiles and Standard deviation?

A school system employs teachers at salaries between 30,000 and 60,000. The teachers' union and the school board are negotiating the form of next year's increase in the salary schedule. Suppose that every teacher is given a flat 1000 raise.


a) How much will the mean salary increase? Median salary?





b) Will a flat 1000 dollar raise increase the spread as measured by the distance between the quartiles? explain?





c) Will a flat 1000 dollar raise increase the spread as measured by the standard deviation of the salaries? Explain?

Mean, Quartiles and Standard deviation?
How much will the mean salary increase? Median salary?





well if there were 3 teachers then mean is





(a+b+c)/3





after pay rise its


(a+1000+b+1000+c+1000)/3


(a+b+c+3000)/3


(a+b+c)/3 + 1000





The mean goes up by 1000


The rankings dont change so the person being paid the median rate still gets paid the median rate (which obviously has gone up by 1000





b) Will a flat 1000 dollar raise increase the spread as measured by the distance between the quartiles? explain?





The spread will not change. IQR+UQ-LQ





after this is (UQ+1000)-(LQ+1000)=UQ-LQ





c) Will a flat 1000 dollar raise increase the spread as measured by the standard deviation of the salaries? Explain?





The SD is the average distance of each score from the mean, so on average scores are still the same distance from the mean so no it wont change.