Why does changing an x-value affect the mean but not the variation?

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SUMMARY

Changing an x-value in a dataset affects the mean but does not impact the variation when all values are shifted by the same amount. The mean is calculated as the average of the values, which directly responds to changes in individual x-values. In contrast, variance measures the dispersion of values around the mean, remaining unchanged when all values are uniformly adjusted. This distinction is crucial for understanding statistical behavior in data analysis.

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bob4000
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mathematically why does the mean change when an x-value is changed in a list, but the variation doesn't. if someone could show me a relevant formula which can satisfy this or any other info i would be very grateful for

thnak you
 
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If you change all the values on the list by the same amount, the mean changes with it, but the variance, which measures the fluctuations around the mean doesn't change. If you shift one value only, both the mean and the variance will change.
 

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