A construction worker checked the number of screws needed to complete 7 jobs. He counted:20 screws53 screws13 screws53 screws62 screws35 screws93 screwsWhat was the mean absolute deviation of the numbers of screws needed?If the answer is a decimal, round it to the nearest tenth.mean absolute deviation (MAD): screwsSubmit
Question
A construction worker checked the number of screws needed to complete 7 jobs. He counted:20 screws53 screws13 screws53 screws62 screws35 screws93 screwsWhat was the mean absolute deviation of the numbers of screws needed?If the answer is a decimal, round it to the nearest tenth.mean absolute deviation (MAD): screwsSubmit
Solution
To find the mean absolute deviation (MAD), we first need to find the mean (average) of the data set.
Step 1: Find the mean Add up all the numbers: 20 + 53 + 13 + 53 + 62 + 35 + 93 = 329 Then divide by the number of data points, which is 7: 329 / 7 = 47
Step 2: Find the absolute deviations Subtract the mean from each number in the data set and take the absolute value of the result. This gives us the absolute deviations: |20 - 47| = 27 |53 - 47| = 6 |13 - 47| = 34 |53 - 47| = 6 |62 - 47| = 15 |35 - 47| = 12 |93 - 47| = 46
Step 3: Find the mean of the absolute deviations Add up all the absolute deviations: 27 + 6 + 34 + 6 + 15 + 12 + 46 = 146 Then divide by the number of data points, which is 7: 146 / 7 = 20.9
So, the mean absolute deviation (MAD) of the numbers of screws needed is approximately 20.9 screws.
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