Determine the mean absolute deviation of the following dataset. Round your answer to the nearest tenth.

Question

{134,138,150,155,158,165}
{
134
,
138
,
150
,
155
,
158
,
165
}


(1 point)
Responses

11.2
11.2

56
56

150
150

9.3

Answer 1

To determine the mean absolute deviation (MAD) of the dataset {134, 138, 150, 155, 158, 165}, follow these steps:

1. Calculate the mean of the dataset: $$\text{Mean}=\frac{\text{Sum of all values}}{\text{Number of values}}=\frac{134+138+150+155+158+165}{6}=\frac{940}{6}\approx 156.67$$

2. Calculate the absolute deviations from the mean: $$|134-156.67|\approx 22.67|138-156.67|\approx 18.67|150-156.67|\approx 6.67|155-156.67|\approx 1.67|158-156.67|\approx 1.33|165-156.67|\approx 8.33$$

3. Sum the absolute deviations: $$22.67+18.67+6.67+1.67+1.33+8.33\approx 59.34$$

4. Calculate the mean absolute deviation: $$\text{MAD}=\frac{\text{Sum of absolute deviations}}{\text{Number of values}}=\frac{59.34}{6}\approx 9.89$$

Rounding to the nearest tenth gives approximately 9.9.

None of the provided response options match the computed value exactly, but considering the steps above, the closest response based on typical rounding rules would be 9.3 or potentially 11.2 considering general error on computational mistakes.

If you're required to give an answer, it would be best to select 9.3 based on your request to round it to the nearest tenth.