Question

Consider a dataset with at least three values. Suppose the highest value is increased by 5 and the lowest is decreased by 2. Which of the following measure(s) would not change?

	a.	Mean
	b.	Standard deviation
	c.	Median
	d.	a and b

Answer 1

Solution-

Median is not changed if highest is increased by 5 and smallest is decresesd by 2

So, Option c. Median is correct.

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For more simplicity we can calculate using dataset

1st dataset is - 4,5,6,7

Mean = 5.5, Median = 5.5 , standard deviation =1.29

Now, lowest value is decreased by 2 and highest value is increased by 5-

​​​​​​2nd dataset is = 2,5,6,12

Mean = 6.25 , Median = 5.5 , standard deviation = 4.19

So, by above we can see Mean and standard deviation are changed but Median is not changed.