The accompanying data represent the miles per gallon of a random sample of cars

Question

The accompanying data represent the miles per gallon of a random sample of cars with a three-cylinder, 1.0 liter engine (a) Compute the z-score corresponding to the individual who obtained 40.7 miles per gallon. Interpret this result. (b) Determine the quartiles, (c) Compute and interpret the interquartile range, IQR. (d) Determine the lower and upper fences. Are there any outiers? 31.3 35.8 38.0 38.6 40.4 42 34.0 36.2 38.1 38.9 40.7 42.8 34.4 37.4 38.2 39.1 413 43.6 35.4 37.6 38.5 39.2417 49.1 EE Click the icon to view the data.

Explanation / Answer

a)
Mean = 38.8500
std.dev. = 3.6597

z = (40.7 - 38.8500)/(3.6597/sqrt(24)) = 2.4765

score 40.7 lies to 2.4765 times standard error from the mean

b)

median = 38.55

Q1 = 36.8

Q3 = 41

c)

IQR = Q3 - Q1 = 41 - 36.8 = 4.2

d)

lower fence = 38.55 - 3*4.2 = 25.95

upper fence = 38.55 + 3*4.2 = 51.15

There are no outliers

1 31.3 2 34 3 34.4 4 35.4 5 35.8 6 36.2 7 37.4 8 37.6 9 38 10 38.1 11 38.2 12 38.5 13 38.6 14 38.9 15 39.1 16 39.2 17 40.4 18 40.7 19 41.3 20 41.7 21 42.1 22 42.8 23 43.6 24 49.1

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