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)

z = (40.7 - 38.4333)/(4.154/sqrt(24)) = 2.6732

b)

Quartile 1 = 36.00 (Average of 6th and 7th)

Quartile 3 = 41.00 (Average of 18th and 19th)

Median = 38.35 (Average of 12th and 13th)

c)

IQR = 41 - 36 = 5

d)

lower fence = 38.35 - 3*5 = 23.35

upper fence = 38.35 + 3*5 = 43.35

Two outliers 43.6 and 49.1

Mean 38.4333 std. dev. 4.1540

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