The number of words Mr. Ahmad’s students read per minute is 109, 89, 112, 98, 101, 105, 120, 106. What is the mean absolute deviation of the dataset? Round the answer to the nearest tenth
To find the mean absolute deviation (MAD) of the dataset, we need to find the mean and then subtract each value from the mean, take the absolute value, and find the average of those differences.
First, we find the mean:
Mean = (109 + 89 + 112 + 98 + 101 + 105 + 120 + 106) / 8
Mean = 840 / 8
Mean = 105
Next, we find the differences between each value and the mean:
|109 - 105| = 4
|89 - 105| = 16
|112 - 105| = 7
|98 - 105| = 7
|101 - 105| = 4
|105 - 105| = 0
|120 - 105| = 15
|106 - 105| = 1
Next, we find the average of these differences:
(4 + 16 + 7 + 7 + 4 + 0 + 15 + 1) / 8
54/8
6.75
Therefore, the mean absolute deviation (MAD) of the dataset is 6.8 (rounded to the nearest tenth).
To find the mean absolute deviation (MAD) of a dataset, follow these steps:
Step 1: Calculate the mean (average) of the data set.
To calculate the mean, add up all the numbers in the data set and divide the sum by the total number of values.
Sum of the numbers = 109 + 89 + 112 + 98 + 101 + 105 + 120 + 106 = 840
Total number of values = 8
Mean = Sum of the numbers / Total number of values = 840 / 8 = 105
Step 2: Calculate the absolute deviation for each value in the data set.
To calculate the absolute deviation, subtract the mean from each value in the data set. Ignore the positive or negative sign of the result.
Absolute deviations: |109 - 105|, |89 - 105|, |112 - 105|, |98 - 105|, |101 - 105|, |105 - 105|, |120 - 105|, |106 - 105|
Absolute deviations: 4, 16, 7, 7, 4, 0, 15, 1
Step 3: Calculate the mean of the absolute deviations.
To calculate the mean of the absolute deviations, add up all the absolute deviations and divide the sum by the total number of values.
Sum of the absolute deviations = 4 + 16 + 7 + 7 + 4 + 0 + 15 + 1 = 54
Total number of values = 8
Mean of absolute deviations = Sum of the absolute deviations / Total number of values = 54 / 8 = 6.75
Therefore, the mean absolute deviation of the dataset is approximately 6.8 when rounded to the nearest tenth.