Two random samples of 25 people were asked how many 12-ounce cans of soda they consume each week. the first sample contained both males and females, aged 12-19. the second sample contained both males and females, aged 20-39. the results are shown in the table below. sample #1 16 11 9 12 11 10 10 8 15 0 2 15 14 7 11 5 14 20 3 11 13 7 0 5 21 sample #2 18 14 0 7 5 7 10 7 6 9 12 3 14 4 11 16 0 10 9 5 0 16 11 2 4 part 1: find the mean of sample #1. part 2: find the mean absolute deviation of sample #1.

neither question asks about sample 2.

sample 1

1 16 11 9 12 11 10 10 8 15 0 2 15 14 7 11 5 14 20 3 11 13 7 0 5 21

i count 26 items

adding those up, we get 251

answer, part 1:   mean = 251/26 = 9.654

part 2,

let's call the mean u = 251/26

for the mean absolute deviation, we calculate

mad = (1/26) {   |1 - u| + |16 - u| + |11 - u| + + | 21-u|   }

for all the elements bigger than u the absolute value doesn't do anything.

for the elements less than u the absolute value negates things.

let's sort into two categories,  

< u: 1 9 8 0 2 7 5 3 7 0 5         count 11, sum 47

> u: 16 11 12 11 10 10 15 15 14 11 14 20 11 13 21       count 15, sum 204

so the total absolute deviation is for the first list is 11u - 47 and the

total for the second list is 204 - 15u for a mean absolute deviation

mad = (1/26)(204 - 15u + 11u - 47)= (1/26)(157 - 4(251/26))

mad = 1539/338   ≈ 4.553

answer: mad 4.553

quit

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