Please someone explain mean absolute deviation and give an example because I have to solve this one question that asks of me to find the mean absolute deviation of 49, 55, 52, 46, 47, 42, and 38 and I don't understand what it is.
https://www.google.com/search?client=safari&rls=en&q=mean+absolute+deviation+definition&ie=UTF-8&oe=UTF-8
^ Thanks.
Sure! Mean Absolute Deviation (MAD) is a statistical measure that calculates the average absolute difference between each data point and the mean of the dataset. It provides a measure of dispersion or how much the data values deviate from the mean.
To find the MAD, you need to follow these steps:
Step 1: Find the mean (average) of the dataset.
To do this, add up all the values and then divide the sum by the total number of values in the dataset.
Mean = (49 + 55 + 52 + 46 + 47 + 42 + 38) / 7 = 369 / 7 = 52.71 (rounded to two decimal places)
Step 2: Find the absolute difference between each data point and the mean.
To do this, subtract the mean from each data point and take the absolute value of the result. The absolute value disregards the sign and gives you a non-negative value.
Absolute difference from the mean:
|49 - 52.71| = 3.71
|55 - 52.71| = 2.29
|52 - 52.71| = 0.71
|46 - 52.71| = 6.71
|47 - 52.71| = 5.71
|42 - 52.71| = 10.71
|38 - 52.71| = 14.71
Step 3: Find the average of the absolute differences.
Sum up all the absolute differences and divide the total by the number of values in the dataset.
MAD = (3.71 + 2.29 + 0.71 + 6.71 + 5.71 + 10.71 + 14.71) / 7 = 44.55 / 7 = 6.36 (rounded to two decimal places)
The mean absolute deviation of the dataset 49, 55, 52, 46, 47, 42, and 38 is approximately 6.36. This means, on average, each data point deviates from the mean by approximately 6.36.