Statistics math 227

Question

Listed below are the top 10 annual salaries (in millions of dollars) of TV personalities. Find the range, variance, and standard deviation for the sample data. Given that these are the top 10 salaries, do we know anything about the variation of salaries of TV personalities in general?

38 36 35 27 17 13 11 7 6.9 6.4

Answer 1

Hi Habiba,

Great question! Here are a few tips to help you out:

Range: List the numbers in order (ascending or descending...you choose) and take the HIGHEST number minus the LOWEST number. This number gives you the spread of the top 10 annual salaries.

Variance σ²: This number measures variability or how far members within a set of numbers are spread out. First, you should find the mean (average) of the data set. Then, subtract the mean from each number within the data set and square this number. Last, sum all of these numbers and divide by the total number of data points within your data set. Let me get you started with this particular example:

Mean (X) = (38+36+35+27+17+13+11+7+6.9+6.4)/10

(38-X)² =...

(36-X)² =...

(35-X)² = ...

Then add all of these numbers together and divide by 10 (the total number of data points in the set)... and VOILA!

Standard Deviation: Easy... just take the square root of the Variance!