Ashley saved money every month last year. The table below shows how much money she saved each month.
Dollars Saved
Month Money Saved (in dollars)
January 96
February 38
March 162
April 65
May 178
June 112
July 57
August 143
September 135
October 104
November 88
December 22
What is the mean absolute deviation of the amounts she saved?
A.
18
B.
39
C.
23
D.
156
To find the mean absolute deviation, we need to calculate the mean and then find the absolute deviation for each value and average those.
First, let's calculate the mean:
Mean = (96+38+162+65+178+112+57+143+135+104+88+22) / 12 = 1096 / 12 = 91.333 (rounded to the nearest thousandth)
Next, let's find the absolute deviation for each value and sum them:
Absolute Deviation = |96-91.333| + |38-91.333| + |162-91.333| + |65-91.333| + |178-91.333| + |112-91.333| + |57-91.333| + |143-91.333| + |135-91.333| + |104-91.333| + |88-91.333| + |22-91.333|
= 4.667 + 53.333 + 70.667 + 26.333 + 86.667 + 20.667 + 34.333 + 51.667 + 43.667 + 12.667 + 3.333 + 69.333
= 477.000
Finally, divide the sum of the absolute deviations by the number of values (12) to find the mean absolute deviation:
Mean Absolute Deviation = 477 / 12 = 39.750
The mean absolute deviation of the amounts Ashley saved is approximately 39. Therefore, the correct answer is B.