Serge had the following scores on his math tests last quarter. 100,94,78,88,87,93,96,and 92.Find the mean absolute deviation for the set of data.
First, you want to put them in order from least to greatest, so it should me Order: 78,88,87,92,93,94,96,100. You want to start by finding the mean, which the average of the dated divided by the number of numbers in the set. Find the absolute value of the difference between each data value and the mean: (data value – mean).Find the sum of the absolute values of the differences. Divide the sum of the absolute values of the differences by the number of data values.
Thank you, Kassie
Yes, thank you Kassie :)
To find the mean absolute deviation (MAD), you need to follow these steps:
1. Calculate the mean of the data set. The mean is found by adding up all the values and dividing the sum by the number of values.
In this case, the sum of the scores is:
100 + 94 + 78 + 88 + 87 + 93 + 96 + 92 = 728
And since there are 8 scores, the mean is:
728 / 8 = 91
2. Find the absolute deviation for each score. To do this, subtract the mean from each score and take the absolute value (ignoring the negative sign, if any).
The absolute deviations for each score are:
|100 - 91| = 9
|94 - 91| = 3
|78 - 91| = 13
|88 - 91| = 3
|87 - 91| = 4
|93 - 91| = 2
|96 - 91| = 5
|92 - 91| = 1
3. Calculate the average absolute deviation. Add up all the absolute deviations and divide the sum by the number of scores.
The sum of the absolute deviations is:
9 + 3 + 13 + 3 + 4 + 2 + 5 + 1 = 40
Since there are 8 scores, the mean absolute deviation is:
40 / 8 = 5
Therefore, the mean absolute deviation for the given set of data is 5.