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.
I apologize for the error in my previous response.
To find the sum of the absolute deviations, we can calculate the absolute value of the difference between each data point and the mean, and then sum those values.
The differences from the mean are:
|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
Summing these absolute deviations, we get: 15.1 + 22.9 + 26.1 + 4.1 + 15.1 + 35.9 + 1.9 ≈ 121.1
Rounded to the nearest tenth, the sum of the absolute deviations in the dataset is 121.1.
To find the sum of the absolute deviations, we calculate the absolute value of the difference between each data point and the mean, and then sum those values.
The differences from the mean are:
|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
Summing these values, we get: 15.1 + 22.9 + 26.1 + 4.1 + 15.1 + 35.9 + 1.9 = 120.1
Rounded to the nearest tenth, the sum of the absolute deviations in the dataset is 120.1.
WRONG
To find the sum of the absolute deviations, 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 of each data point from the mean:
- For the data point 63, the absolute deviation is |63 - 47.9| = 15.1
- For the data point 25, the absolute deviation is |25 - 47.9| = 22.9
- For the data point 74, the absolute deviation is |74 - 47.9| = 26.1
- For the data point 52, the absolute deviation is |52 - 47.9| = 4.1
- For the data point 63, the absolute deviation is |63 - 47.9| = 15.1
- For the data point 12, the absolute deviation is |12 - 47.9| = 35.9
- For the data point 46, the absolute deviation is |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
So, the sum of the absolute deviations is 120.1 rounded to the nearest tenth.