Question

In: Statistics and Probability

Which of the following is true of variance? a. Its value is inversely proportional to the...

Which of the following is true of variance?

a.

Its value is inversely proportional to the degree to which the data is spread from the mean.
b.

The formula to calculate variance of a population is not the same as the formula to calculate variance of a sample.
c.

It is the square root of standard deviation.
d.

It only requires the middle 50% of data to be calculated

Solutions

Expert Solution

Solution:

We have to identify the correct or true statement about the variance.

Variance is directly  proportional to the degree to which the data is spread from the mean, because as the spread of data values from the mean increases, then variance is also increases.

Variance is the square of standard deviation, not the square root of standard deviation.

Variance is based on all observations in the data, not just the middle 50% of data.

Thus option a, c and d are incorrect.

Formula for  variance of a population is:

Formula for  variance of a sample is:

Thus both formulas are different.

Thus correct statement about variance is:

b. The formula to calculate variance of a population is not the same as the formula to calculate variance of a sample.

orchestra answered 2 years ago
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