Question

There are two fast food burger chains near your house. You want to determine which one has the shortest wait times. The last ten times you went to “Dan’s Diner,” the wait times were:

12, 13, 13, 16, 17, 19, 19, 20, 22, 24 (minutes)

You then call the statistician for “Burger Barn” and he tells you the following:
“Our mean wait time is 19 minutes, with a standard deviation of 1.65 minutes. Here is

our 5-number summary: {12, 18, 19, 20, 25}”
a.) (2 pts.) Write a 5-number summary {min, Q1, median, Q3, max} for Dan’s Diner.

b.) (3 pts.) Draw box plots for Dan’s Diner and Burger Barn on the same number line (one above the other).

c.) (3 pts.) Compare the two box plots. Which restaurant has shorter wait times? Use statistical language in your answer.

d.) (3 pts.) Complete the table and calculate the standard deviation for Dan’s Diner. Dan’s Diner: 12, 13, 13, 16, 17, 19, 19, 20, 22, 24

Data value	Deviation	Squared Deviation

Standard Deviation (round to two decimal places):

e.) (3 pts.) Which burger chain has more consistent wait times? Use statistical language in your answer.

Answer 1

(a) 5 number summary for Dan's Diner. Detailed calculation is given in the image below

(b) Boxplot:

(c) Observe above two boxplots. First quartile, and median for Dan's Diner is less than that of Burger Barn. So median waiting time for Dan's Diner is less than that of Burger Barn. Interquartile range(IQR) is Third quartile minus first quartile which is more for Dan's Diner. IQR measures the spread of the data, more the IQR more is the spread of the data from mean. Boxplot clearly shows that Dan's Diner has shorter wait times.

(d) Standard deviation is 4.03. Table and detailed solution is in the image below

(e) Burger Barn has more consistent wait times.

Standard deviation measure the spread of the data. More the standard deviation, more is the spread and more spread means data is less consistent. Standard deviation for Burger Barn is 1.65 minutes and standard deviation for Dan's Diner is 4.03. Hence Burger Barn has more consistent waiting time than Dan's Diner.

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