mean deviation - A small car dealership tests the fuel efficiency of sedans on its lot. It chooses 12 sedans for the test. The fuel efficiency (mpg) values of the cars are given in the table below. Complete the table as directed below

Sangeetha Pulapaka (last edited 1 year ago) (Expert, Educator @Qalaxia)

Step 1: Recall on how to calculate the mean

\frac{29 +35+24+25+21+21+18+28+31+26+26+22}{12} = 25.5

Step 2: Subtract the given mean from the mean got above to get the deviations from the mean

29 - 25.5 = 3.5

35 - 25.5 = 9.5

24 - 25.5 = -1.5

25 - 25.5 = -0.5

21 - 25.5 = -4.5 etc.

Doing this we get the values

Step 3: Recall on how to square values

Square the values got above to get

Step 4: Find the sum of the squared deviations

Recall on how to add more than two decimals

Add 12.25 +90.25 + 2.25 +0.25 +20.25 +56.25 +6.25 + 30.25 + 0.25 +12.25 to get

251

Step 5: Calculate the mean of this data set

n = 12

\frac{251}{11}= 22.818 to the nearest thousndth.

Which is also the variance, since

[squaring deviation from the mean] ÷ number of observations = variance