## 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 1 Answer 0 views 0

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!