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, we subtract the mean from each data point and take the absolute value. Then, we sum up those absolute deviations.
First, let's find the differences between each data point and 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
Next, let's take the absolute value of each difference:
|15.1| = 15.1
|-22.9| = 22.9
|26.1| = 26.1
|4.1| = 4.1
|15.1| = 15.1
|-35.9| = 35.9
|-1.9| = 1.9
Finally, let's 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 is 120.1. Rounding to the nearest tenth, the answer is 120.1. Answer: \boxed{120.1}.
wrong
Apologies for the mistake. To find the sum of the absolute deviations, we subtract the mean from each data point, take the absolute value, and then sum them up.
Let's calculate the absolute deviation for each data point:
|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
Now let's sum up these absolute deviations:
15.1 + 22.9 + 26.1 + 4.1 + 15.1 + 35.9 + 1.9 = 120.0
Therefore, the sum of the absolute deviations is 120.0. Answer: \boxed{120.0}.
still wrong
Apologies for the continued mistake. Let's recalculate the sum of the absolute deviations correctly.
To find the absolute deviation for each data point, we subtract the mean from each data point and take the absolute value:
|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
Now let's sum up these absolute deviations:
15.1 + 22.9 + 26.1 + 4.1 + 15.1 + 35.9 + 1.9 = 121.1
Therefore, the correct sum of the absolute deviations is 121.1. Rounding to the nearest tenth, the answer is 121.1.
To find the sum of the absolute deviations in a dataset, you need to find the absolute deviation for each data point from the mean, and then sum them up.
1. Find the absolute deviation for each data point by subtracting the mean from each data point and taking the absolute value:
- Absolute deviation for 63: |63 - 47.9| = 15.1
- Absolute deviation for 25: |25 - 47.9| = 22.9
- Absolute deviation for 74: |74 - 47.9| = 26.1
- Absolute deviation for 52: |52 - 47.9| = 4.1
- Absolute deviation for 63: |63 - 47.9| = 15.1
- Absolute deviation for 12: |12 - 47.9| = 35.9
- Absolute deviation for 46: |46 - 47.9| = 1.9
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, follow these steps:
1. Subtract the mean from each data point.
For the given dataset, subtract 47.9 from each number:
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
2. Take the absolute value of each result. Ignore the negative signs.
The absolute values of the differences are:
15.1, 22.9, 26.1, 4.1, 15.1, 35.9, 1.9
3. Add up all the absolute values.
Summing up these absolute values, we get:
15.1 + 22.9 + 26.1 + 4.1 + 15.1 + 35.9 + 1.9 = 120.2
So, the sum of the absolute deviations in the given dataset is 120.2 (rounded to the nearest tenth).