The weekly salaries (in dollars) for 9 employees of a small business are given below.
(Note that these are already ordered from least to greatest.)
559, 652, 686, 755, 758, 765, 833, 853, 1105
Send data to calculator
Suppose that the $1105 salary changes to $925. Answer the following.
(a)
What happens to the median?
(b)
What happens to the mean?
• It decreases by
• It increases by
• It stays the same.
• It decreases by
• It increases by
• It stays the same.

(a) The median remains the same at 758.

(b) The mean decreases by 20 dollars, from 774 to 754.

Would you like further details or clarifications?

Here are 5 related questions for further practice:
1. How does changing the highest salary affect the range of the dataset?
2. What happens to the standard deviation when the highest salary changes?
3. How would the mode be impacted if the dataset had repeated salaries?
4. How would adding a new employee with a salary of 600 affect the median?
5. What is the interquartile range (IQR) for the original dataset?

**Tip:** The median is resistant to extreme values, but the mean is sensitive to changes in outliers.

The weekly salaries (in dollars) for 9 employees of a small business are given below. (Note that these are already ordered from least to greatest.) 559, 652, 686, 755, 758, 765, 833, 853, 1105. Suppose that the $1105 salary changes to $925. Answer the following: (a) What happens to the median? (b) What happens to the mean?

This problem analyzes the effect of adjusting the highest salary on the mean and median of a dataset of employee salaries. It demonstrates that the median remains unaffected, while the mean decreases due to the change in the extreme value. Ideal for students in Grades 7-10 studying statistics and data analysis.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation