Math Problem Statement
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.
Solution
(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:
- How does changing the highest salary affect the range of the dataset?
- What happens to the standard deviation when the highest salary changes?
- How would the mode be impacted if the dataset had repeated salaries?
- How would adding a new employee with a salary of 600 affect the median?
- 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.
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Math Problem Analysis
Mathematical Concepts
Statistics
Mean
Median
Impact of Outliers
Formulas
Mean = (sum of all values) / (number of values)
Median = middle value of an ordered dataset
Theorems
Mean is sensitive to changes in extreme values
Median is resistant to changes in extreme values
Suitable Grade Level
Grades 7-10
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