Answer:
To find the mean absolute deviation (MAD) of a data set, you need to follow these steps:
- Find the mean of the data set.
- For each data point, find the absolute value of the difference between the data point and the mean.
- 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:
- Find the mean: mean = (10 + 10 + 15 + 15 + 16 + 18 + 23) / 7 = 15.71
- 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).