Required information Section 01.02 Exercise 14 - Effects of changing data values on mean, median, and standard deviation There are 14 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.

Question

Mathematics

Gabriel Decker

22 November, 20:11

Required information Section 01.02 Exercise 14 - Effects of changing data values on mean, median, and standard deviation There are 14 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.

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Erin Gonzalez · Answer 1

Mean will Increase. Median remains unchanged. Standard deviation will increase.

Step-by-step explanation:

We are given that there are 14 employees in a particular division of a company and their salaries have a mean of $70,000, a median of $55,000, and a standard deviation of $20,000.

And also the largest number on the list is $100,000 but By accident, this number is changed to $1,000,000.

Now we have to analyse the Effect of this change in data values on mean, median, and standard deviation.

Mean will get affected because $1,000,000 is a very huge value as compared to $100,000 and is considered to be an outlier and we know that mean is affected by outliers as mean will change to $134285.7143 after replacing $100,000 with $1,000,000. Median will not get affected as median the middle most value in the data set and since $1,000,000 is considered to be an outlier so median remain unchanged at $55,000. Standard Deviation will also get affected as due to outlier value in the data set the numerator value will increase very much and due to which standard deviation will also increase.