If the data set {5, 7, 8, 9, 10} has a mean of 7.8, what is the sum of the devia

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Question: If the data set {5, 7, 8, 9, 10} has a mean of 7.8, what is the sum of the deviations from the mean?

Options:

Correct Answer: 0

Solution:

The sum of deviations from the mean is always 0.

If the data set {5, 7, 8, 9, 10} has a mean of 7.8, what is the sum of the deviations from the mean?

If the data set {5, 7, 8, 9, 10} has a mean of 7.8, what is the sum of the deviations from the mean?

Correct Answer: 0

Step 1: Understand what 'deviation from the mean' means. It is how far each number in the data set is from the mean (average).
Step 2: Calculate the mean of the data set {5, 7, 8, 9, 10}. The mean is given as 7.8.
Step 3: Find the deviation for each number in the data set by subtracting the mean from each number:
- For 5: 5 - 7.8 = -2.8
- For 7: 7 - 7.8 = -0.8
- For 8: 8 - 7.8 = 0.2
- For 9: 9 - 7.8 = 1.2
- For 10: 10 - 7.8 = 2.2
Step 4: Add all the deviations together: -2.8 + (-0.8) + 0.2 + 1.2 + 2.2.
Step 5: Calculate the sum: -2.8 - 0.8 + 0.2 + 1.2 + 2.2 = 0.
Step 6: Conclude that the sum of the deviations from the mean is always 0.

Mean and Deviations – Understanding that the sum of deviations from the mean in any data set is always zero.