1

Problem

Calculate the Mean Absolute Deviation (MAD) for the weekly temperatures in Celsius: 22, 24, 23, 25, 27, 26, and 21.

2

Step

Given weekly temperatures:

22, 24, 23, 25, 27, 26, and 21

3

Step

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

\$Mean = (22 + 24 + 23 + 25 + 27 + 26 + 21) / 7\$
\$Mean = (168)/(7)\$ = 24

4

Step

The mean temperature is 24 degrees Celsius.

5

Step

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

\$\∣22 - 24\∣ = 2\$
\$\∣24 - 24\∣ = 0\$
\$\∣23 - 24\∣ = 1\$
\$\∣25 - 24\∣ = 1\$
\$\∣27 - 24\∣ = 3\$
\$\∣26 - 24\∣ = 2\$
\$\∣21 - 24\∣ = 3\$

6

Step

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

The sum of absolute deviations = 2 + 0 + 1 + 1 + 3 + 2 + 3 = 12

7

Step

Calculate the Mean of the Absolute Deviations:

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

→ \$(12) / 7\$ = 1.71

8

Solution

Therefore, the Mean Absolute Deviation (MAD) for the weekly temperatures is approximately 1.71 degrees Celsius.

9

Sumup

Please summarize steps

Choices

10

Choice-A

This value is very close to our calculated mean absolute deviation (MAD) of 1.71, but it is slightly lower. The precise calculation gives 1.71, so 1.69 is not accurate

Wrong 1.69 degrees

11

Choice-B

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

Correct 1.71 degrees

12

Choice-C

This value is higher than our calculated MAD. While it might seem close, it is not as close as option A, and it significantly deviates from the exact calculated value of 1.71. Therefore, this is not the correct option

Wrong 1.78 degrees

13

Choice-D

This value is lower than both our calculated MAD and the slightly incorrect option A (1.69). It deviates more significantly from the correct MAD of 1.71, making it incorrect

Wrong 1.63 degrees

14

Answer

Option

B

15

Sumup

Please summarize choices