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 43.4 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 outliers?

(a) Compute the z-score corresponding to the individual who obtained 43.4 miles per gallon. Interpret this result.

The z-score corresponding to the individual is _______  and indicates that the data value is _______  standard deviation(s) the _______ 

Answer 1

Mean = (32.3 + 36.1 + 37.9 + 38.7 + 39.8 + 42.5 + 34.3 + 36.3 + 38.1 + 38.9 + 40.6 + 42.7 + 34.6 + 37.4 + 38.3 + 39.6 + 41.4 + 43.4 + 35.5 + 37.7 + 38.5 + 39.8 + 41.6 + 48.9)/24 = 38.954

standard deviation = sqrt(((32.3 - 38.954)^2 + (36.1 - 38.954)^2 + (37.9 - 38.954)^2 + (38.7 - 38.954)^2 + (39.8 - 38.954)^2 + (42.5 - 38.954)^2 + (34.3 - 38.954)^2 + (36.3 - 38.954)^2 + (38.1 - 38.954)^2 + (38.9 - 38.954)^2 + (40.6 - 38.954)^2 + (42.7 - 38.954)^2 + (34.6 - 38.954)^2 + (37.4 - 38.954)^2 + (38.3 - 38.954)^2 + (39.6 - 38.954)^2 + (41.4 - 38.954)^2 + (43.4 - 38.954)^2 + (35.5 - 38.954)^2 + (37.7 - 38.954)^2 + (38.5 - 38.954)^2 + (39.8 - 38.954)^2 + (41.6 - 38.954)^2 + (48.9 - 38.954)^2)/23) = 3.498

a) z-score = (x - mean)/SD

                = (43.4 - 38.954)/3.498

                = 1.27

The z-score corresponding to the individual is 1.27 and indicates that the data value is 1.27 standard deviations above the mean.

b) Q1 = (36.3 + 37.4)/2 = 36.85

    Q2 = (38.5 + 38.7)/2 = 38.6

    Q3 = (40.6 + 41.4)/2 = 41

c) IQR = Q3 - Q1 = 41 - 36.85 = 4.15

d) Lower fence = Q1 - 1.5 * IQR

                         = 36.85 - 1.5 * 4.15

                         = 30.625

Upper fence = Q3 + 1.5 * IQR

                     = 41 + 1.5 * 4.15

                     = 47.225

Yes, there is an outlier. The outlier is 48.9