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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There are 12 employees in a particular division of a company. Their salaries ha a median of $48,000, and a standard deviation of $18,000. The largest number 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?

There are 12 employees in a particular division of a company. Their salaries ha a median of $48,000, and a standard deviation of $18,000. The largest number 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?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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Topic Video

Question

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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