Question

Listed below are the amounts​ (dollars) it costs for marriage proposal packages at different baseball stadiums. Find the​ range, variance, and standard deviation for the given sample data. Include appropriate units in the results. Are there any​ outliers, and are they likely to have much of an effect on the measures of​ variation?

36 50 50 55 55 90 95 115 195 206 250 325 500 2000 2500

Answer 1

36 50 50 55 55 90 95 115 195 206 250 325 500 2000 2500

Data is in increasing order already, so we skip the step of arranging in increasing order.

Now,

Range = Maximum - minimum = 2500 - 36 = 2464

Variance =  

We need to first find mean of the data set.

mean = = (36 + 50 +......+2500) / 15 = 434.8

Now variance = [ (36-434.8)^2 +...........+(2500-434.8)^2 ] / 14 = 568251.2

Standard deviation = = = 753.8244

Outlier: Data value that is numerically distant from a data set.

So, 2000 and 2500 are the outliers.

Without the outliers, mean = 155.5

Since Variance =

It contains mean in its formula, so the variance is affected by outliers.