For the data set {2, 4, 6, 8, 10}, what is the mean deviation?

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Question: For the data set {2, 4, 6, 8, 10}, what is the mean deviation?

Options:

Correct Answer: 1.6

Solution:

Mean = 6; Mean deviation = (|2-6| + |4-6| + |6-6| + |8-6| + |10-6|)/5 = (4 + 2 + 0 + 2 + 4)/5 = 12/5 = 2.4.

For the data set {2, 4, 6, 8, 10}, what is the mean deviation?

For the data set {2, 4, 6, 8, 10}, what is the mean deviation?

Step 1: Find the mean of the data set {2, 4, 6, 8, 10}.
Step 2: Add all the numbers together: 2 + 4 + 6 + 8 + 10 = 30.
Step 3: Count how many numbers are in the data set. There are 5 numbers.
Step 4: Divide the total sum by the count of numbers to find the mean: 30 / 5 = 6.
Step 5: Calculate the absolute deviations from the mean for each number: |2-6|, |4-6|, |6-6|, |8-6|, |10-6|.
Step 6: Calculate each absolute deviation: |2-6| = 4, |4-6| = 2, |6-6| = 0, |8-6| = 2, |10-6| = 4.
Step 7: Add all the absolute deviations together: 4 + 2 + 0 + 2 + 4 = 12.
Step 8: Divide the total absolute deviation by the number of data points to find the mean deviation: 12 / 5 = 2.4.

Mean – The average of a set of numbers, calculated by summing the values and dividing by the count.
Mean Deviation – A measure of dispersion that calculates the average of the absolute differences between each data point and the mean.
Absolute Value – The non-negative value of a number without regard to its sign, used in calculating mean deviation.