What is the sum of the absolute deviations in the following dataset: 63, 25, 74, 52, 63, 12, 46? The mean of the dataset is 47.9. Round to the nearest tenth.(1 point)
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What is the sum of the absolute deviations in the following dataset: 63, 25, 74, 52, 63, 12, 46? The mean of the dataset is 47.9. Round to the nearest tenth.(1 point)
To find the sum of the absolute deviations in the dataset, we need to calculate the absolute deviation of each data point from the mean and then sum them up.
Step 1: Calculate the absolute deviation for each data point:
- For 63: |63 - 47.9| = 15.1
- For 25: |25 - 47.9| = 22.9
- For 74: |74 - 47.9| = 26.1
- For 52: |52 - 47.9| = 4.1
- For 63: |63 - 47.9| = 15.1
- For 12: |12 - 47.9| = 35.9
- For 46: |46 - 47.9| = 1.9
Step 2: Sum up the absolute deviations:
15.1 + 22.9 + 26.1 + 4.1 + 15.1 + 35.9 + 1.9 = 120.1
Therefore, the sum of the absolute deviations in the given dataset is 120.1.
To find the sum of the absolute deviations in a dataset, you need to calculate the absolute value of the difference between each data point and the mean, and then sum up all these absolute values.
1. Calculate the absolute deviation for each data point:
- For 63: |63 - 47.9| = 15.1
- For 25: |25 - 47.9| = 22.9
- For 74: |74 - 47.9| = 26.1
- For 52: |52 - 47.9| = 4.1
- For 63: |63 - 47.9| = 15.1
- For 12: |12 - 47.9| = 35.9
- For 46: |46 - 47.9| = 1.9
2. Sum up all the absolute deviations:
15.1 + 22.9 + 26.1 + 4.1 + 15.1 + 35.9 + 1.9 = 120.1
So, the sum of the absolute deviations in the given dataset is 120.1. Rounded to the nearest tenth, it is 120.1.
The sum of the absolute deviations is 229.9.
To find this, we first need to calculate the absolute deviation of each data point from the mean:
|63 - 47.9| = 15.1
|25 - 47.9| = 22.9
|74 - 47.9| = 26.1
|52 - 47.9| = 4.1
|63 - 47.9| = 15.1
|12 - 47.9| = 35.9
|46 - 47.9| = 1.9
Then we add up all of these absolute deviations:
15.1 + 22.9 + 26.1 + 4.1 + 15.1 + 35.9 + 1.9 = 229.9
Rounded to the nearest tenth, we get 229.9.