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 40.4 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? MPG Data 32.8 35.9 37.8 38.540.4 42.2 34.6 36.4 37.9 38.9 40.6 42.8 34.8 37.3 38.39.2 41.4 43.3 35.4 37.5 38.3 39.7 41.6 49.1 EEB Click the icon to view the data. (a) Compute the z-score corresponding to the individual who obtained 40.4 miles per gallon. Interpret this result. The z-score corresponding to the individual is and indicates that the data value isstandard deviation(s)the Type integers or decimals rounded to two decimal places as needed.) Print Done (b) Determine the quartiles. Q1mpg Type an integer or a decimal. Do not round.) Q2mpg Type an integer or a decimal. Do not round.) (Type an integer or a decimal. Do not round.)

Explanation / Answer

Solution:

z score=x-mean/sd

sample mean=38.9375

samplesd= 3.46897

Z=40.4-38.9375/ 3.46897

Z=0.42

AND THE DATA VALUE IS

0.42 STANDARD DEVIATIONS ABOVE MEAN

Solutionb:

code in R to get the required answer:

MPG <- c(32.8,35.9,37.8,38.5,40.4,42.2,34.6,36.4,37.9,38.9,40.6,42.8,34.8,37.3,38.1,39.2,41.4,43.3
,35.4,37.5,38.3,39.7,41.6,49.1)
print(MPG)
quantile(MPG,0.25)

Q1=37.075

quantile(MPG,0.50)

Q2=38.4

quantile(MPG,0.75)

Q3=40.8

Solutionc:

IQR=Q3-Q1

=40.8-37.075

= 3.725

THE INTERQUARTILE RANGE IS 3.725.IT IS THE RANGE OF MIDDLE 50% OF THE OBSERVATIONS IN THE Datset

ANSWERS GIOVEN IN BOLD

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