Exploring the Impact of Changing Mean and Standard Deviation on Median and Mode

[yukcream]

Will the median and mode change if the mean and strandard deviation change?

 

[HallsofIvy]

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.

 

[CRGreathouse]

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

 

[HallsofIvy]

And, by the way, standard deviation has nothing to do with mean, median, or mode!