Answered

Find and interpret the mean absolute deviation of the data.



$25,28,20,22,32,28,35,34,30,36$



The mean absolute deviation is

.



The values differ from the mean by an average of

.

Verified Answer :

e3van22

To find the mean absolute deviation (MAD), we first need to find the mean of the data set:

Mean = (25 + 28 + 20 + 22 + 32 + 28 + 35 + 34 + 30 + 36) / 10

    = 290 / 10

    = 29

Now, we find the absolute deviation for each data point by subtracting the mean from each value and taking the absolute value:

|25 - 29| = 4

|28 - 29| = 1

|20 - 29| = 9

|22 - 29| = 7

|32 - 29| = 3

|28 - 29| = 1

|35 - 29| = 6

|34 - 29| = 5

|30 - 29| = 1

|36 - 29| = 7

Next, we find the average of these absolute deviations:

MAD = (4 + 1 + 9 + 7 + 3 + 1 + 6 + 5 + 1 + 7) / 10

   = 44 / 10

   = 4.4

Therefore, the mean absolute deviation is 4.4.

Interpretation: On average, the values in the data set differ from the mean by approximately 4.4 units. This indicates the typical amount of variation or spread in the data set.

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