Will Changes in Mean and Standard Deviation Affect Median and Mode?

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Homework Help Overview

The discussion revolves around the relationship between mean, median, mode, and standard deviation in a set of data. Participants explore whether changes in mean and standard deviation impact the median and mode.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Some participants provide examples of data sets to illustrate how mean, median, and mode can differ, questioning the interdependence of these measures of central tendency. Others raise the point that standard deviation does not influence the mean, median, or mode.

Discussion Status

The discussion is active, with participants sharing examples and clarifying concepts. There is an exploration of different scenarios where mean, median, and mode can vary independently, and some guidance is offered regarding the nature of standard deviation in relation to these measures.

Contextual Notes

Participants are considering various data sets and their characteristics, while also addressing assumptions about the relationships between these statistical measures.

yukcream
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Will the median and mode change if the mean and strandard deviation change?
 
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They might, they might not. "mean" is one measure of "central tendency", median and mode are others. It is easy to think up examples of collections of data that have different means but the same median and mode. It's even easier to think up examples of collections of data in which all three are different.
 
yukcream said:
Will the median and mode change if the mean and strandard deviation change?

mean(1,1,1,1,5,6,7,8,9) = 39/9 = 4.3333...
median(1,1,1,1,5,6,7,8,9) = 5
mode(1,1,1,1,5,6,7,8,9) = 1

mean(1,1,1,2,5,6,7,8,9) = 40/9 = 4.4444...
median(1,1,1,2,5,6,7,8,9) = 5
mode(1,1,1,2,5,6,7,8,9) = 1

mean(1,1,2,2,2,6,7,8,9) = 38/9 = 4.2222...
median(1,1,2,2,2,6,7,8,9) = 2
mode(1,1,2,2,2,6,7,8,9) = 2

mean(1,2,2,2,2,6,7,8,9) = 39/9 = 4.3333...
median(1,2,2,2,2,6,7,8,9) = 2
mode(1,2,2,2,2,6,7,8,9) = 2
 
And, by the way, standard deviation has nothing to do with mean, median, or mode!
 

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