Mean Deviation Calculator

B

The mean is 33.9. The mean deviation is the absolute values of the deviation from the mean. (0.1 + 1.1 + 7.1 + 5.9 + 7.9 + 4.9 + 1.9 + 2.1 + 4.1 + 6.1)/10 =

41.2/10 = 4.12

To calculate the mean deviation, also known as the mean absolute deviation (MAD), you need to follow these steps:

Step 1: Find the mean (average) of the ratings.

To find the mean, add up all the ratings and divide the sum by the total number of ratings:

Mean = (34 + 35 + 41 + 28 + 26 + 29 + 32 + 36 + 38 + 40) / 10 = 339 / 10 = 33.9

Step 2: Calculate the deviation of each rating from the mean.

To calculate the deviation, subtract the mean from each individual rating. The deviation measures how far each rating is from the mean:

Deviation = Rating - Mean

For example, the deviation for the first rating (34) would be:

Deviation = 34 - 33.9 = 0.1

Repeat this calculation for each rating:

34 - 33.9 = 0.1 35 - 33.9 = 1.1 41 - 33.9 = 7.1 28 - 33.9 = -5.9 26 - 33.9 = -7.9 29 - 33.9 = -4.9 32 - 33.9 = -1.9 36 - 33.9 = 2.1 38 - 33.9 = 4.1 40 - 33.9 = 6.1

Step 3: Calculate the absolute value of each deviation.

Take the absolute value of each deviation to ensure that all values are positive. Absolute values disregard the direction (positive or negative) of the deviations.

For example, the absolute value of the first deviation (0.1) is:

|0.1| = 0.1

Repeat this calculation for each deviation:

|0.1| = 0.1 |1.1| = 1.1 |7.1| = 7.1 |-5.9| = 5.9 |-7.9| = 7.9 |-4.9| = 4.9 |-1.9| = 1.9 |2.1| = 2.1 |4.1| = 4.1 |6.1| = 6.1

Step 4: Find the mean of the absolute deviations.

To find the mean of the absolute deviations, add up all the absolute deviations and divide the sum by the total number of deviations:

Mean Deviation = (0.1 + 1.1 + 7.1 + 5.9 + 7.9 + 4.9 + 1.9 + 2.1 + 4.1 + 6.1) / 10 = 41.1 / 10 = 4.11

The mean deviation of the ratings is 4.11.

Comparing this with the given answer choices, we see that the closest option is B. 4.12. Therefore, the correct answer is B. 4.12.