Sample Variance Formula

The sample variance better known as s2 is utilized to evaluate the extent of fluctuation or variation in the sample. A specimen or sample is a selected number of elements brought out from a population. For instance, if somebody is assessing the load or the weight of Americans, it is not likely from a moment or currency perspective for them to assess the weight of every person in the population.

The sample variance is assessed comparative to the average or means of the database. It is furthermore named an estimated variance.

Since databases can be of two categories, widely known as grouped and ungrouped, two procedures or formulas can be utilized to evaluate sample variance. Similarly, if the square root of the sample variance is calculated it will result in the sample standard deviation. In this summary, vivid detail of the sample variance and its formula accompanied by various examples are provided.

• Sample variance is provided by the formula or the equation which is

    S2 = (X-x)2n-1, where n represents the amount or the number of categories

• For the sample, one wields n – 1 in the procedure or the formula because utilizing n provides a prejudiced conclusion that invariably miscalculates the variability

• The sample variance verges to be shorter than the real variance of the community or the population

• Curtailing the specimen or the sample n to n – 1 gives rise to the variance artificially huge, providing an unbiased or unbiased conclusion of the variability, rather than overvaluing rather than undervaluing the variability of the specimen or the sample

• It is crucial to point out that performing a similar thing with the standard deviation procedure or formula does not transpire in an entirely unbiased conclusion

• Since the square root is not a linear undertaking, such as expansion or reduction, the unbiasedness of the specimen or the sample variance formula does not hold or carry over from the specimen or sample standard deviation formula

Example: 

There are a total of 45 pupils in a particular class. Out of them, 5 pupils were erratically chosen from this grade and their heights (cm) were documented as emerges:

Sample size (n) = 5

Sample Mean = (131 + 148 + 139 + 142 +152) / 5 = 712 / 5 = 142.4 cm

Using the sample variance formula,

Sample Variance =  i=(xi-n)2n-1 = i=15(xi-142.4)25-1

= [(131−142.4)2+(148−142.4)2+(139−142.4)2+(142−142.4)2+(152−142.4)2] / 4 = 66.3 cm2

Result:  Sample Mean is 142.4 cm whereas Sample Variance is 66.3 cm2.

Important formulas: