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.
