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For the data set 62, 73, 74, 75, 76, the mean is 72. What is the mean absolute deviation?

A. The mean absolute deviation is 5.
B. The mean absolute deviation is 4.
C. The mean absolute deviation is 20.
D. The mean absolute deviation is 72.

Sagot :

GinnyAnswer
To determine the mean absolute deviation (MAD) for the given data set (62, 73, 74, 75, 76) with a mean of 72, follow these detailed steps:

1. Calculate the deviations from the mean for each data point:
- For 62: [tex]\( |62 - 72| = 10 \)[/tex]
- For 73: [tex]\( |73 - 72| = 1 \)[/tex]
- For 74: [tex]\( |74 - 72| = 2 \)[/tex]
- For 75: [tex]\( |75 - 72| = 3 \)[/tex]
- For 76: [tex]\( |76 - 72| = 4 \)[/tex]

So, the absolute deviations from the mean are: [tex]\( 10, 1, 2, 3, 4 \)[/tex].

2. Sum these absolute deviations:
[tex]\[ 10 + 1 + 2 + 3 + 4 = 20 \][/tex]

3. Find the number of data points:
The number of data points in this set is 5.

4. Calculate the mean absolute deviation:
The mean absolute deviation (MAD) is the sum of the absolute deviations divided by the number of data points.
[tex]\[ \text{MAD} = \frac{\sum \text{Absolute Deviations}}{\text{Number of Data Points}} = \frac{20}{5} = 4 \][/tex]

Therefore, the mean absolute deviation is 4.

Answer: B. The mean absolute deviation is 4.
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