Find the range, variance, and standard deviation for the sample data.

Question

Listed below are the gross amounts (in millions of dollars) earned in box office receipts for a recent movie. The amounts are listed in order for the first 14 days of the movies release. Find the range, variance, and standard deviation for the sample data. If you invested in this movie, what characteristic of the data set would you care about most, and is it a measure of center or variation?

 

57, 46, 44, 38, 36, 32, 32, 30, 25, 14, 14, 13, 21, 11

Answer 1

The range is the highest number in the data set minus the lowest number:  57 - 11 = _____

 

The variance is ∑(x-μ)²/n where:

• ∑ is the sum of all the (x-μ)² values
• x is each value on your data set (57, 46, etc...)
• μ is the mean or average of your data set (add the data up then divide by 14)
• n is the number of items in your data set = 14

 

To find the variance:

• First compute the average (μ) of your data set by adding up all of the numbers then dividing by the number of items in the list (14)
• Next, compute (x-μ)² for each data item (x) in the list.  You have 14 data items so you need to make the calculation for all 14 data items.
• Add up all of the fourteen (x-μ)² numbers you computed
• Divide the sum by n, the number of data items in your list (n=14)

 

The standard deviation is the square root of the variance, √(variance)