Question

Find the mean absolute deviation of each data set. Round each answer to two decimal places.

10,10,15,15,16,18,23

Answer 1

To find the mean absolute deviation (MAD) of a data set, you need to follow these steps:

1. Find the mean of the data set.
2. For each data point, find the absolute value of the difference between the data point and the mean.
3. Find the mean of the absolute differences to get the MAD.

Using the data set 10, 10, 15, 15, 16, 18, 23, we can calculate the MAD as follows:

1. Find the mean: mean = (10 + 10 + 15 + 15 + 16 + 18 + 23) / 7 = 15.71
2. Find the absolute difference between each data point and the mean:

|10 - 15.71| = 5.71

|10 - 15.71| = 5.71

|15 - 15.71| = 0.71

|15 - 15.71| = 0.71

|16 - 15.71| = 0.29

|18 - 15.71| = 2.29

|23 - 15.71| = 7.29

3. Find the mean of the absolute differences:

MAD = (5.71 + 5.71 + 0.71 + 0.71 + 0.29 + 2.29 + 7.29) / 7 = 3.71

Therefore, the mean absolute deviation of the data set 10, 10, 15, 15, 16, 18, 23 is 3.71 (rounded to two decimal places).

Answer 2

To find the mean absolute deviation, follow these steps:

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

mean = (10 + 10 + 15 + 15 + 16 + 18 + 23) / 7

mean = 107 / 7

mean = 15.29

2. Find the absolute deviation of each data point by subtracting the mean from the data point and taking the absolute value.

|10 - 15.29| = 5.29

|10 - 15.29| = 5.29

|15 - 15.29| = 0.29

|15 - 15.29| = 0.29

|16 - 15.29| = 0.71

|18 - 15.29| = 2.71

|23 - 15.29| = 7.71

3. Find the mean of the absolute deviations.

mean absolute deviation = (5.29 + 5.29 + 0.29 + 0.29 + 0.71 + 2.71 + 7.71) / 7

mean absolute deviation = 22.29 / 7

mean absolute deviation = 3.18

Therefore, the mean absolute deviation of the data set is 3.18.