Find the mean deviation about the mean for the data. 5, 10, 15, 20, 25.
6
The mean deviation about the mean measures the average distance of the data values from their mean. Its formula is:
Mean deviation = (Σ |xᵢ − mean|) / n, where the vertical bars denote the absolute value (distance, always taken as positive), and n is the number of observations.
Absolute values are essential here: without them the positive and negative deviations would cancel out and always give zero, which is why we ignore direction and add up only the sizes of the gaps.
Step 1 — Find the mean. Mean = (5 + 10 + 15 + 20 + 25) / 5 = 75 / 5 = 15.
Step 2 — Find the absolute deviation of each value from 15.
- |5 − 15| = 10
- |10 − 15| = 5
- |15 − 15| = 0
- |20 − 15| = 5
- |25 − 15| = 10
Step 3 — Average these deviations. Sum = 10 + 5 + 0 + 5 + 10 = 30. Mean deviation = 30 / 5 = 6.
Hence the correct answer is 6. Answers such as 5, 7 or 8 arise from arithmetic slips — for instance, forgetting the middle term of 0, mis-adding the deviations, or dividing by the wrong count.
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Important Questions from Elementary Statistics
In a colony 5 families have 1 child, 7 families have 2 children, 8 families have 3 children and 3 families have 4 children.What is the mode of the number of children.
What will be the difference between mean and median of the given data?
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For which set of numbers do the mean, median and mode all have the same value?
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