The number of apples produced per tree in Zara’s orchard is 125, 198, 209, 213, 101, 178. What is the mean absolute deviation of the dataset? Round to the nearest tenth.(1 point)
First, we need to find the mean of the dataset:
mean = (125 + 198 + 209 + 213 + 101 + 178) / 6
mean = 151.33
Next, we need to find the absolute deviation of each value from the mean:
|125 - 151.33| = 26.33
|198 - 151.33| = 46.67
|209 - 151.33| = 57.67
|213 - 151.33| = 61.67
|101 - 151.33| = 50.33
|178 - 151.33| = 26.67
Then, we find the mean of these absolute deviations:
mean absolute deviation = (26.33 + 46.67 + 57.67 + 61.67 + 50.33 + 26.67) / 6
mean absolute deviation = 42.11
Rounded to the nearest tenth, the mean absolute deviation of the dataset is 42.1.
To find the mean absolute deviation (MAD) of a dataset, follow these steps:
1. Find the mean (average) of the dataset.
125 + 198 + 209 + 213 + 101 + 178 = 1024
1024 ÷ 6 = 170.7 (rounded to the nearest tenth)
2. Find the absolute value of the difference between each data point and the mean.
125 - 170.7 = 45.7
198 - 170.7 = 27.3
209 - 170.7 = 38.3
213 - 170.7 = 42.3
101 - 170.7 = 69.7
178 - 170.7 = 7.3
3. Find the mean of the absolute values calculated above.
(45.7 + 27.3 + 38.3 + 42.3 + 69.7 + 7.3) ÷ 6 = 39.4 (rounded to the nearest tenth)
Therefore, the mean absolute deviation (MAD) of the dataset is approximately 39.4.