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How do we find the mean absolute deviation of a data set?
F
We are given a table that shows the number of calories in twelve different snacks.
| Number of Calories in Snacks | |||
|---|---|---|---|
| 122 | 91 | 149 | 121 |
| 64 | 138 | 342 | 72 |
| 179 | 105 | 99 | 114 |
We are asked to find the mean absolute deviation. Let's recall the formula to find it.
Add terms
Calculate quotient
Now we can find the absolute value of the difference between each data value and the mean. Let's do it!
| x_i | |x - x_i| | Simplify |
|---|---|---|
| 122 | |133 - 122| | 11 |
| 91 | |133 - 91| | 42 |
| 149 | |133 - 149| | 16 |
| 121 | |133 - 121| | 12 |
| 64 | |133 - 64| | 69 |
| 138 | |133 - 138| | 5 |
| 342 | |133 - 342| | 209 |
| 72 | |133 - 72| | 61 |
| 179 | |133 - 179| | 46 |
| 105 | |133 - 105| | 28 |
| 99 | |133 - 99| | 34 |
| 114 | |133 - 114| | 19 |
Now let's add all of these values together and divide the sum by 12 to find the mean absolute deviation.
Add terms
Calculate quotient
The mean absolute deviation of the calories of each snack is 46 calories. Therefore, the correct answer is F.