Question

Calculate the MAD
2.75, 3.20, 3.50, 355, 3.75, 3.80, 400, 545

Answer 1

To calculate the Mean Absolute Deviation (MAD), you need to find the mean of the data set, subtract the mean from each data point to find the deviations, take the absolute value of each deviation, and find the mean of the absolute deviations.

Step-by-step explanation:

The MAD (Mean Absolute Deviation) is a measure of the average distance between each data point and the mean. To calculate the MAD, follow these steps:

1. Find the mean of the data set.
2. Subtract the mean from each data point to find the deviations.
3. Take the absolute value of each deviation.
4. Find the mean of the absolute deviations to get the MAD.

For the given data set, the mean is 184.6. The deviations from the mean are:

2.75 - 184.6 = -181.85

3.20 - 184.6 = -181.4

3.50 - 184.6 = -181.1

355 - 184.6 = 170.4

3.75 - 184.6 = -180.85

3.80 - 184.6 = -180.8

400 - 184.6 = 215.4

545 - 184.6 = 360.4

The absolute deviations are:

181.85, 181.4, 181.1, 170.4, 180.85, 180.8, 215.4, 360.4

The mean of the absolute deviations is:

(181.85 + 181.4 + 181.1 + 170.4 + 180.85 + 180.8 + 215.4 + 360.4) / 8 = 370.5

Therefore, the MAD of the given data set is 370.5.