## There are 10 employees in a particular division of a company. Their salaries have a mean of $70,000, a median of $55,000, and a standard dev

Question

There are 10 employees in a particular division of a company. Their salaries have a mean of $70,000, a median of $55,000, and a standard deviation of $20,000. The largest number on the list is $100,000. By accident, this number is changed to $1,000,000.

a.What is the mean after the change?

b.What is the value of the median after the change?

c.What is the value of the standard deviation after the change?

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3 months
2022-02-17T19:04:09+00:00
2022-02-17T19:04:09+00:00 1 Answer
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## Answers ( )

Answer:a) $700, 000

b) $550, 000

c) $200, 000

Step-by-step explanation:By symmetric principle. What happen is just a stretch in the length of scale of the distribution. Initially, we stopped at maximum of $100, 000. The scale was accidentally extended by a multiple of 10 => $1000, 000. The whole curve will automatically extends too; shifting the mean, median and standard deviation by the same measure of multiple!

A good point to make is that, the question didn’t tell us that the sample size (n) increases. It means that the sample size (n) is still = 10 employees. The only error was that, their salaries was accidentally multiply by $10.

If you are familiar with R programming, try this illustration on you own:

###############################

x = c(2,3,4,5,6,7,8,9,1,3)

mean(x)

median(x)

sd(x)

max(x)

#… now, let’s multiply by 10

x = c(20,30,40,50,60,70,80,90,10,30)

mean(x)

median(x)

sd(x)

max(x)

###############################

The results are exactly a multiple of 10!