Variance given Frequency Table

Variance from a Frequency Table

Sometimes we are given a frequency table instead of a long list of repeated values and are asked to find the variance of the data set.

​Variance of Frequency Distributions

Suppose x₁​, x₂ , . . . , x_m have respective frequencies f₁ , f₂ , . . . , f_m , then

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Given the frequency table, find the variance.

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x	f
​1	10​
4​	20​
7​	30​
10​	40​

​x	​f
​10	​4
​14	​6
​18	​8
​22	​2

​Given the frequency table, find the variance.