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.
First, we need to find the mean of the dataset:
Mean = (125 + 198 + 209 + 213 + 101 + 178) / 6 = 156.5
Next, we need to find the deviation from the mean for each data point:
Deviation from mean for 125: |125 - 156.5| = 31.5
Deviation from mean for 198: |198 - 156.5| = 41.5
Deviation from mean for 209: |209 - 156.5| = 52.5
Deviation from mean for 213: |213 - 156.5| = 56.5
Deviation from mean for 101: |101 - 156.5| = 55.5
Deviation from mean for 178: |178 - 156.5| = 21.5
Now we need to find the average of these deviations, which is the mean absolute deviation:
Mean Absolute Deviation = (31.5 + 41.5 + 52.5 + 56.5 + 55.5 + 21.5) / 6 ≈ 45.8
Therefore, the mean absolute deviation of the dataset is approximately 45.8.
To find the mean absolute deviation (MAD) of a dataset, follow these steps:
Step 1: Find the mean (average) of the dataset.
Step 2: Subtract the mean from each value in the dataset to get the deviation.
Step 3: Take the absolute value of each deviation.
Step 4: Find the mean of the absolute deviations to get the MAD.
Let's calculate the MAD step-by-step:
Step 1: Find the mean (average) of the dataset.
Adding up the numbers: 125 + 198 + 209 + 213 + 101 + 178 = 1024.
Divide the sum by the number of values: 1024 ÷ 6 = 170.67 (rounded to two decimal places).
Step 2: Subtract the mean from each value in the dataset to get the deviation.
125 - 170.67 = -45.67,
198 - 170.67 = 27.33,
209 - 170.67 = 38.33,
213 - 170.67 = 42.33,
101 - 170.67 = -69.67,
178 - 170.67 = 7.33.
Step 3: Take the absolute value of each deviation.
|-45.67| = 45.67,
|27.33| = 27.33,
|38.33| = 38.33,
|42.33| = 42.33,
|-69.67| = 69.67,
|7.33| = 7.33.
Step 4: Find the mean of the absolute deviations to get the MAD.
Adding up the absolute deviations: 45.67 + 27.33 + 38.33 + 42.33 + 69.67 + 7.33 = 230.66.
Divide the sum by the number of values: 230.66 ÷ 6 = 38.44 (rounded to two decimal places).
Therefore, the mean absolute deviation (MAD) of the dataset is approximately 38.4.