There are 12 employees in a particular division of a company. Their salaries have a mean of $65,000,a median of $48,000, and a standard deviation of $18,000. The largest number on the list is $100,000. Byaccident, this number is changed to $300,000.a. What is the value of 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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Description: There are 12 employees in a particular division of a company. Their salaries have a mean of $65,000,a median of $48,000, and a standard deviation of $18,000. The largest number on the list is $100,000. Byaccident, this number is changed to $300,000.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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There are 12 employees in a particular division of a company. Their salaries have a mean of $65,000,
a median of $48,000, and a standard deviation of $18,000. The largest number on the list is $100,000. By
accident, this number is changed to $300,000.
a. What is the value of 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?

Expert Solution

Step 1

Given:

Mean salary of 12 employees = $ 65,000

Median salary of 12 employees = $ 48,000

Standard deviation of salary of 12 employees = $ 18,000

Largest number = $ 100,000

(a) Sum of salary of 12 employees = $12 \times 65000 = 780000$

Since, $ 100,000 was changed to $ 300,000

The increase in salary of 12 employees = $ (300,000 - 100,000) = $ 200,000

Therefore,

New sum of salary of 12 employees = Initial sum + Increased salary

= $ (780000+200000)

= $ 980000

So, new average salary after the change = $\frac{N e w s u m o f s a l a r y o f 12 e m p l o y e e s}{12}$

$= \frac{980000}{12} = 81666.6667$

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