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 37 36 30 19 17 14 13 12.6 12.0

Answer 1

The range is the difference between the smallest and the highest value.

$$38-12.0=26$$

The mean is: 

$$mean=\bar{x}=\frac{1}{10}(38 +37+ 36+ 30+ 19+ 17$$ $$+14 +13+ 12.6+ 12.0)=22.86$$

The variance is:

$$Variance=s^2=\frac{1}{10-1}((38-22.86)^2+(37-22.86)^2$$

$$+(36-22.86)^2+(30-22.86)^2+(19-22.86)^2$$

$$+(17-22.86)^2+(14-22.86)^2+(13-22.86)^2$$

$$+(12.6-22.86)^2+(12.0-22.86)^2)=122.329333$$

The standard variation is

$$s=\sqrt{s^2}=\sqrt{122.329333}=11.060259$$

$$range=26$$

$$mean=22.86$$

$$Variance=122.33$$

$$standard\ deviation=11.06$$

No, because the sample is not representative of the whole population.