Management knows that the longer shoppers stay in a store, the more likely a pur

Question

Management knows that the longer shoppers stay in a store, the more likely a purchase will be made. Management has asked you to do a study of the length of time in minute that people shop in you store. One of your staff members randomly selects 5 shoppers and records the number of minutes they are in the store. The time in minutes for the 5 random shoppers are:

                Time Spent in Shopping (minutes)

                                10

                                18

                                12

                                170

                                25

                For statistical purposes while it would aid in what management wants to show, the

statistician does not want to use the data point of 170 minutes (just under 3 hours in the

store). Since it is considerably more than the others, the statistician feels that when this

time was recorded, the staff member by mistake, added a zero (0) making 17 minutes 170

minutes. Some random information you may or may not need: Mean =47 minutes,

Median= 18 minutes, Variance= 4,762 minutes. How would you respond to the statistician? (Provide rationale)

**** Please show your work/steps and advise what theory/formula used to solve problem; Thanks!****

Explanation / Answer

Let us decide whether to agree with the statistician or not, by assessing statistically whether 170 is an outlier or not. Let's use IQR method to find out the outliers.

IQR method:

Step 1. Arrange the data in ascending order [10, 12, 18, 25, 170]

Step 2. Calculate first quartile (Q1), third quartile (Q3) and the interquartile range (IQR=Q3-Q1)

Q1 is the median of the numbers in the left of the median of the original data, i.e., the median of [10,12]. Since only two data points are there, mean of them is to be considered as the median. Hence Q1 = (10+12)/2 = 11

Similarly Q3 is the median of the numbers in the right of the median of the original data, hence Q3 = (25+170)/2 = 97.5

Thus IQR = 97.5 - 11 = 86.5

Step 3. Compute Q1–1.5 × IQR (=-118.75), and Q3+1.5 × IQR (=227.25) Anything outside this range is an outlier

Since 170 clearly falls within the range [Q1-1.5IQR, Q3+1.5IQR], it is not an outlier. Thus we should recommend the statistician to reconsider his/her decision to exclude 170 from any further analyses.

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