4. Miami-Dade County Public Schools employs teachers at salaries between $40,000 and $71,000. The teachers’ union and the school board are negotiating the form of next year’s increase in the salary schedule. (a) If every teacher is given a flat $1000 raise, what will this do to the mean salary? To the median salary? Explain your answers. (b) What would a flat $1000 raise do to the extremes and quartiles of the salary distribution? To the standard deviation of teachers’ salaries? Explain your answers.

a. Mean and Median will increase by $1,000.

If every teacher was to see their salary increase by $1,000 then the mean will also increase by $1,000 because each data value in the set increased by $1,000 but the number of teachers did not.

The Median will also increase by 1,000 because with all the values increasing by the same number, the middle position will still be the same but will have increased by $1,000.

b. The Extremes and the Quartiles will increase by $1,000

Quartiles like medians are simply positions occupied by a number in the data set. If all values increase by the same amount, the numbers occupying the quartile positions will increase by $1,000 as well. The same goes for the extremes.

Standard deviation will remain the same.

Standard deviation measures the dispersion around the mean. If the both the mean and the data values increase by the same amount, the dispersion will remain the same as the increases will cancel each other out.

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