Question

MPG
36.3
41
36.9
37.1
44.9
36.8
30
37.2
42.1
36.7
32.7
37.3
41.2
36.6
32.9
36.5
33.2
37.4
37.5
33.6

1. The EPA collects data on 20 cars and calculates their gas mileage in miles per gallon (MPG).

a) Make a histogram for the data with the first class of [30, 32).

b) Find the mean, the median and the standard deviation of the data.

c) Find the Q1, Q3, IQR and fences.

d) Using the modified box-plot methodology determine if there are any outliers and justify. You do not have to make the box-plot!

e) Create a new variable by subtracting the mean from each observation and then dividing the difference by the standard deviation.

f) Find the mean, median and standard deviation of the new variable.

g) In one or two sentences, describe the original data.

Answer 1

a)

b)

mean = 36.895

median = 36.85

sd = 3.5074

c)

Q1 = 34.95

Q3 = 37.45

IQR = Q3- Q1 = 2.5

lower fence =Q1 - 1.5 IQR = 34.95 - 1.5 * 2.5 = 31.2

Upeer fence = Q3 +1.5 IQR = 37.45 + 1.5 * 2.5 = 41.2

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