How does the variance of the sample mean compare to the variance of the population? Multiple Choice It is smaller and therefore suggests that averages have less variation than individual observations. It is larger and therefore suggests that averages have less variation than individual observations. It is smaller and therefore suggests that averages have more variation than individual observations. It is larger and therefore suggests that averages have more variation than individual observations.

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Mathematics

Sabrina Maddox

18 November, 14:46

How does the variance of the sample mean compare to the variance of the population? Multiple Choice It is smaller and therefore suggests that averages have less variation than individual observations. It is larger and therefore suggests that averages have less variation than individual observations. It is smaller and therefore suggests that averages have more variation than individual observations. It is larger and therefore suggests that averages have more variation than individual observations.

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Paloma Bowman · Answer 1

It is larger and therefore suggests that averages have more variation than individual observations.

Step-by-step explanation:

Variance is a measure of dispersion of data from sample mean.

Population variance is a measure of this dispersion in entire population. Sample variance is a measure of this dispersion in the sample.

Population variance is the : sum of squared deviations from mean / N Sample variance is : sum of squared deviations from mean / n - 1

[where N & n are number of units in population, sample respectively]

So, the denominators of population & sample variances state that, sample variance > population variance.

So, sample averages have more variation than individual observations.