Question

The accompanying data represent the miles per gallon of a random sample dI cars with a three-cylinder, 1.0 liter engine.

(a) Compute the z-score corresponding to the individual who obtained 32.7 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 outliers?

(a) Compute the z-score corresponding to the individual who obtained 32.7 miles per gallon. Interpret this result.

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

Answer 1

a) The mean of the given sample is calculated by

And Standard deviation as

S is calculated as 3.502

Z score is calculated as

Interpretation:

The Z score corresponding to the individual score is -1.79 Standard deviation below the Mean.

b) The Sample is already in ascending order

Hence, The Quartiles are

Minimum=32.7

Q1= 36.85

Q2=38.65

Q3=41

Maximum=49.1

c) IQR is the Inter Quartile Range calculated as

Q3-Q1=41-36.85=4.15

d) The Lower fence is calculated as

Q1-1.5*IQR= 36.85-1.5*4.15=30.65

and the Upper fence is calculated as

Q3+1.5*IQR=41+1.5*4.15=47.225

Hence from the fence calculation, it is clear that it has one outlier that is 49.1.