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Sample Variance Formula The sample variance formulas for both types of data are specified below: Ungrouped Data: s2 = ?ni=1(xi??)2n?1 ? i = 1 n ( x i ? ? ) 2 n ? 1. Grouped data: s2 = ?ni=1f(mi?¯¯¯x)2N?1 ? i = 1 n f ( m i ? x ¯ ) 2 N ? 1.
When working with data that are grouped into categories or intervals, the variance and standard deviation are again obtained using the deviations about the mean and the squared value of these. But in this case, the sum of squares of differences1 about the mean are weighted by the number of times each occurs.
Variance(?2)=?(x?¯x)2n=(2?6)2+(4?6)2+(6?6)2+(8?6)2+(10?6)25=(16+4+0+4+16)5=405=8. Q.
Sample variance formula in Excel Find the mean by using the AVERAGE function: =AVERAGE(B2:B7) ... Subtract the average from each number in the sample: ... Square each difference and put the results to column D, beginning in D2: ... Add up the squared differences and divide the result by the number of items in the sample minus 1:
Hear this out loud PauseThe sample variance is defined by(15.59)We use the symbol sx2 for a sample variance and the symbol ?x2 for a population variance.