Each of a sample of 117 residents selected from a small town is asked how much m

Question

Each of a sample of 117 residents selected from a small town is asked how much money he or she spent last week on state lottery tickets. 92 of the residents responded with $0. The mean expenditure for the remaining residents was $19. The largest expenditure was $226. Step

a. What is the range of the data (in dollars)?

b. what is the median?

c.What is the mode?

d.What is the mean of the117data points? Round your answer to one decimal place.

e.What proportion of the sample did not purchase any lottery tickets? Express your answer as a simplified fraction or as a value rounded to one decimal place.

Explanation / Answer

a.) The Range of data is [$0, $226]

b.) Median is the number that is halfway in the data set. To find median we need to arrange our data in ascending or descending order and see the centermost number. Here centermost number qould be $0.

c.) Mode is the value that appears most isn the data set.

d.) We need to take the weighted average.

Sample average = (n1m1 + n2m2) / (n1+n2)

= (92*0 + 25*19) / 117

= $4.05

e.) Fraction that did not purchase any lottery ticket = 92/117

= 0.7

So, the mode here is $0 as it appears the most, 92 times in the data set.

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