A researcher computed the mean, median and standard deviation for a set of performance score. If 5 were to be added to each score, which of these three statistics would change?
Solution
Correct Answer: Option D
First of all, we should understand what each term means. Then the answer would be very
straight-forward. Mean: The average of all values. Median: The value in the center. Standard deviation: Variance is the square root of variance. Variance is the average of the
square of the difference between each value and the mean. Since you add 5 to each value, definitely the average would be n1+5 + n2+5 + n3+5 +... / n ..
where n is the number of values. new mean = (n1+n2+n3+... + 5n) / n
= (n1+n2+ .. ) / n + 5
= old mean + 5 Thus the mean changes by 5. The median is either the middle value in the set (if the number of value
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