1

Problem

Calculate the Mean Absolute Deviation (MAD) for the daily sales (in dollars) recorded over a year: $1200, $1300, $1100, $1400, $1500, $1250, $1350, $1450, $1200, $1300, $1100, and $1400.

2

Step

Given daily sales:

$1200, $1300, $1100, $1400, $1500, $1250, $1350, $1450, $1200, $1300, $1100, and $1400

3

Step

Calculate the Mean (Average): Sum up all the sales and then divide by the number of sales

\$"Mean" = (1200 + 1300 + 1100 + 1400 + 1500 + 1250 + 1350 + 1450 + 1200 + 1300 + 1100 + 1400) / 12\$

\$"Mean" = (15550) / (12)\$ = 1295.83

4

Step

Calculate the Absolute Deviations from the Mean: Find the absolute deviation of each sale from the mean

\$\∣1200 - 1295.83\∣ = 95.83\$
\$\∣1300 - 1295.83\∣ = 4.17\$
\$\1100 - 1295.83\∣ = 195.83\$
\$\∣1400 - 1295.83\∣ = 104.17\$
\$\∣1500 - 1295.83\∣ = 204.17\$
\$\∣1250 - 1295.83\∣ = 45.83\$
\$\∣1350 - 1295.83\∣ = 54.17\$
\$\∣1450 - 1295.83\∣ = 154.17\$
\$\∣1200 - 1295.83\∣ = 95.83\$
\$\∣1300 - 1295.83\∣ = 4.17\$
\$\∣1100 - 1295.83\∣ = 195.83\$
\$\∣1400 - 1295.83\∣ = 104.17\$

5

Step

Sum the absolute deviations and then divide by the number of sales to find the Mean Absolute Deviation (MAD):

The sum of absolute deviations =
95.83 + 4.17 + 195.83 + 104.17 + 204.17 + 45.83 + 54.17
+ 154.17 + 95.83 + 4.17 + 195.83 + 104.17 = 1258.34

6

Step

Calculate the Mean of the Absolute Deviations:

\$MAD = ("Sum of absolute deviations") / ("Number of sales")\$

→ \$(1258.34) / (12)\$ = 104.86

7

Solution

Therefore, the Mean Absolute Deviation (MAD) for the daily sales is approximately $104.86.

8

Sumup

Please summarize steps

Choices

9

Choice-A

This option is incorrect because this value is higher than our calculated MAD (104.86). The precise calculation gives 104.86, so 108.56 is not accurate

Wrong $108.56

10

Choice-B

This option is incorrect because 105.20 is very close to our calculated MAD (104.86), but it is slightly higher. The exact calculation gives 104.86

Wrong $105.20

11

Choice-C

This option is incorrect because the value is too high compared to our calculated MAD, significantly deviating from the exact calculated value of 104.86

Wrong $114.89

12

Choice-D

This value matches our calculated Mean Absolute Deviation exactly. Given our calculation steps and results, this is the correct option

Correct $104.86

13

Answer

Option

D

14

Sumup

Please summarize choices