The list shows the number of songs that five
students each downloaded last week.
32, 43, 38, 28, 51
What is the mean absolute deviation of the
numbers in the list?
A 34.4
B 6.88
C 38.4
D 7.68
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The list shows the number of songs that five students each downloaded last week.
32, 43, 38, 28, 51
What is the mean absolute deviation of the numbers in the list?
To find the mean absolute deviation (MAD), follow these steps:
Step 1: Find the mean (average) of the given set of numbers.
Mean = (32 + 43 + 38 + 28 + 51) / 5 = 192 / 5 = 38.4
Step 2: Subtract the mean from each number and take the absolute value.
|32 - 38.4| = 6.4
|43 - 38.4| = 4.6
|38 - 38.4| = 0.4
|28 - 38.4| = 10.4
|51 - 38.4| = 12.6
Step 3: Find the mean of the absolute differences obtained in step 2.
MAD = (6.4 + 4.6 + 0.4 + 10.4 + 12.6) / 5 = 34.4 / 5 = 6.88
Therefore, the mean absolute deviation of the numbers in the list is 6.88.
The correct answer is B. 6.88.
To find the mean absolute deviation (MAD) of a list of numbers, follow these steps:
1. Find the mean (average) of the numbers in the list:
- Add up all the numbers: 32 + 43 + 38 + 28 + 51 = 192
- Divide the sum by the total number of numbers in the list (which is 5 in this case): 192 / 5 = 38.4
2. Calculate the deviation of each number from the mean:
- Subtract the mean from each number:
- For 32: 32 - 38.4 = -6.4
- For 43: 43 - 38.4 = 4.6
- For 38: 38 - 38.4 = -0.4
- For 28: 28 - 38.4 = -10.4
- For 51: 51 - 38.4 = 12.6
3. Find the absolute value of each deviation (remove any negative sign):
- Absolute value of -6.4 = 6.4
- Absolute value of 4.6 = 4.6
- Absolute value of -0.4 = 0.4
- Absolute value of -10.4 = 10.4
- Absolute value of 12.6 = 12.6
4. Find the mean of the absolute deviations:
- Add up all the absolute deviations: 6.4 + 4.6 + 0.4 + 10.4 + 12.6 = 34.4
- Divide the sum by the total number of numbers in the list (which is 5): 34.4 / 5 = 6.88
Therefore, the mean absolute deviation of the numbers in the list is 6.88. So the correct answer is B) 6.88.