Question

explain in your own words why the formula for the sample variance and sample standard deviation is different from the formulas for the population variance and standard variation.

Answer 1

Answer:

The population variance and population standard deviation are used when calculating for a population while the sample variance and sample standard deviation are used when calculating for a sample

Step-by-step explanation:

A population is defined as all members of a specified group or simply Population is the whole group. A sample is a part of a population that is used to describe the characteristics, The size of a sample can be less than 1%, or 10%, or 60% of the population.

The population variance and population standard deviation are used when calculating for a population while the sample variance and sample standard deviation are used when calculating for a sample. sample variance(or standard deviation) will be slightly higher than that of the population variance(or population standard deviation) for the same problem if solved. The purpose of this little difference it to get an accurate estimate of the population‘s variance to compensate for the fact it is a sample rather than with the whole population.

Answer 2

Answer:

This is to acknowledge the size of the sample is smaller than the size of the entire population and as n becomes larger 'n-1' tends towards n.

Step-by-step explanation:

The variance and the standard deviation calculated from the population data is referred to as the population variance and the population standard deviation while the variance and the standard deviation calculated from the sample data is referred to as the sample variance and the sample standard deviation. The difference in both formulas for the sample and the population is due to the denominator in the formula for the variance of the sample is (n-1) while the denominator is (n) in the formula for the variance of the population.

This therefore makes the variance  and the standard division of the sample to be slightly higher than the variance and the standard deviation of the population. This is so because when we divide by the size of the sample less one (n-1) in the calculation for the sample variance, we are invariably giving grounds for the fact that it is actually a portion of the population that we are working with and not the entire population.