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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

Respuesta :

karlipp0218

Step-by-step explanation:

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

[tex]IQR = Q_{3} - Q_{1}[/tex]

Based on the information provided we fill in:

[tex]IQR = 58 - 45[/tex]

[tex]IQR = 13[/tex]

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

[tex]Q_{1}-1.5[/tex] × [tex]IQR\\[/tex]

[tex]Q_{3}+1.5[/tex] × [tex]IQR\\[/tex]

[tex]1.5[/tex] × [tex]13 = 19.5[/tex]

Now we plugin in:

[tex]45 - 19.5 = 25.5\\[/tex]

[tex]58 + 19.5 = 77.5[/tex]

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.