Final answer:
The mean absolute deviation (MAD) for the group of household incomes, rounded to the nearest tenth, is 15.2 (thousands), which is option C). This is calculated by first finding the mean income, then computing the absolute deviations from the mean for each household, summing them up, and finally dividing by the number of households.
Step-by-step explanation:
Firstly, we must calculate the mean of the given household incomes. Adding all the household incomes together: 38 + 45 + 76 + 93 + 50 + 54 + 29 + 44 + 62 + 31 = 522 (thousands). Since there are 10 households, we divide this sum by 10, which results in a mean income of 52.2 (thousands).
Next, we find the absolute deviations from the mean for each household income, sum them, and then calculate the mean of these absolute deviations:
- 38 - 52.2 = 14.2
- 45 - 52.2 = 7.2
- 76 - 52.2 = 23.8
- 93 - 52.2 = 40.8
- 50 - 52.2 = 2.2
- 54 - 52.2 = 1.8
- 29 - 52.2 = 23.2
- 44 - 52.2 = 8.2
- 62 - 52.2 = 9.8
- 31 - 52.2 = 21.2
The sum of the absolute deviations is 14.2 + 7.2 + 23.8 + 40.8 + 2.2 + 1.8 + 23.2 + 8.2 + 9.8 + 21.2 = 152.4 (thousands). We then divide this sum by the number of household incomes (10) to find the mean absolute deviation (MAD):
152.4 / 10 = 15.24 (thousands)
To answer the question, the mean absolute deviation for the group, when rounded to the nearest tenth, is 15.2 (thousands), which corresponds with option C).