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What is the mean absolute deviation of the following set of data? 3,1,4,4,4,1,1,2,1,5

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Answer:

1.36

Explanation:

1. Find the mean (average) of the data set:

(3 + 1 + 4 + 4 + 4 + 1 + 1 + 2 + 1 + 5) / 10 = 26 / 10 = 2.6

2. Subtract the mean from each data point and take the absolute value of each difference.

|3 - 2.6| = 0.4

|1 - 2.6| = 1.6

|4 - 2.6| = 1.4

|4 - 2.6| = 1.4

|4 - 2.6| = 1.4

|1 - 2.6| = 1.6

|1 - 2.6| = 1.6

|2 - 2.6| = 0.6

|1 - 2.6| = 1.6

|5 - 2.6| = 2.4

Find the mean of these absolute differences:

(0.4 + 1.6 + 1.4 + 1.4 + 1.4 + 1.6 + 1.6 + 0.6 + 1.6 + 2.4) / 10 = 13.6 / 10 = 1.36

So, the mean absolute deviation (MAD) of the given data set is 1.36.

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