The miles per gallon (mpg) for each of 20 medium-sized cars selected from a prod

Question

The miles per gallon (mpg) for each of 20 medium-sized cars selected from a production line during the month of March follow . 23.3 21.5 23.8 23.9 20.4 24.6 25.5 27.2 24.9 22.9 26.4 23.4 26124.9 24.6 24.4 25.1 22.4 23.1 24.8 (a) What are the maximum and minimum miles per gallon? What is the range? maximum I mpg minimum I mpg range mpg (b) Construct a relative frequency histogram for these data. Relative Relative Frequency Frequency 0.25 0.30 0.20 0.20 0.15 0.15 0.10 0.10 0.05 0.05 mpg 2021 2122 2425 26 27 mpg 2021 2122 24 25 26 27 Relative Relative Frequency Frequency 0.25 0.25 0.20 0.15 0.15 0.10 0.10 0.05 0.05 mpg 2021 22 232425 26 27 mpg 20212223 24 25 26 27

Explanation / Answer

a)minimum =20.4

maximum =27.2

range =max-min=6.8

b(top right most curve is right

the distribution is slightly skewed to the left

c) mean =24.16

std deviation=1.6414

d)z score for largest observation =(27.2-24.16)/1.6414 =1.85

z score for smallest observation =(204-24.16)/1.6414 =-2.29

since neither z score is greater then 3 ............

e) median =(n+1)/2 th value =10.5 th value =24.5

f)Q1 =(n+1)/4 th value =5.25 th value =(23.1+0.25*(23.3-23.1)=23.15

Q3 =15.75 th value =24.9+0.75*(25.1-24.9)=25.05

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