Question

Find and interpret the mean absolute deviation of the data.

24, 26, 28, 28, 30, 30, 32, 32, 34,36

Answer 1

To find the mean absolute deviation (MAD) of a set of data, calculate the mean and subtract the mean from each value to find the deviations. Take the absolute value of each deviation, add them up, and divide by the total number of values.

Step-by-step explanation:

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

1. Calculate the mean of the data set by adding up all the values and dividing by the total number of values.
2. Subtract the mean from each individual value to find the deviation from the mean.
3. Take the absolute value of each deviation to eliminate any negative signs.
4. Add up all the absolute deviations.
5. Divide the sum of absolute deviations by the total number of values.

In the given data set (24, 26, 28, 28, 30, 30, 32, 32, 34, 36), the mean is 30. The deviations from the mean are (24-30), (26-30), (28-30), (28-30), (30-30), (30-30), (32-30), (32-30), (34-30), and (36-30), which simplifies to -6, -4, -2, -2, 0, 0, 2, 2, 4, and 6. The absolute deviations are 6, 4, 2, 2, 0, 0, 2, 2, 4, and 6. Adding up all the absolute deviations gives a sum of 28. Dividing this sum by 10 (the total number of values) gives a MAD of 2.8.