Question

1. The number of customers in a restaurant during the peak hour of each day for a month varied

significantly from day to day. Here are pieces of the data on the number of customers served
during the peak hour of each business day:
3 Lowest
25, 32, 37
Q1
45
Mean
48
Median
50
Q3
58
3 highest
69, 70, 75
(a) Are there any outliers in the data set? Justify your answer numerically

Answer 1

Explanation:

First we must calculate the interquartile range (IQR), using this equation:

`IQR = Q_(3) - Q_(1)`

Based on the information provided we fill in:

`IQR = 58 - 45`

`IQR = 13`

In order to find what the range for the data set is we need to use the Interquartile Rule:

`Q_(1)-1.5` ×
`IQR\\`

`Q_(3)+1.5` ×
`IQR\\`

`1.5` ×
`13 = 19.5`

Now we plugin in:

`45 - 19.5 = 25.5\\`

`58 + 19.5 = 77.5`

Any number below 25.5 is a possible outlier and any number above 77.5 is a possible outlier.

Answer:

Based on the results of the calculations, 25 could be a possible outlier in the data set.