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# Momenting around Sample (Mean and Variance)

Let’s understand SAMPLE MEAN and SAMPLE VARIANCE via an example:

Tony owns a plant nursery, and one of his biggest sellers is blueberry bushes. He sells the bushes to his customers when they are at least 18 inches tall. Tony wants to know how long it will take each of his blueberry bushes to grow tall enough to sell.

To get an estimate of this time, he selects ten plants at random and records the number of days each one takes to grow from a seed into an 18-inch tall plant.

Sample Variance

• Another important statistic that can be calculated for a sample is the sample variance.

• Variance measures how spread out the data in a sample is.

• Two samples can have the same mean but be distributed very differently.

• Variance is one way to quantify these differences.

The variance of a sample is also closely related to the standard deviation, which is simply the square root of the variance. The symbol typically used to represent standard deviation is s, so the symbol for variance is s^2.

To find the sample variance, follow these steps:

• First, calculate the sample mean.

• Next, subtract the mean value from the value of each measurement.

• Square the resulting values.

• Add the results together to get the sum of squared deviations from the mean.

• Finally, divide this by the number of degrees of freedom, which is equal to the total number of measurements minus one (n -1)

Note:

• As the sample gets bigger, the variance gets smaller. This should be intuitive since a bigger sample produces more accurate results.

Written by Shreya Golchha ( Graduate in B.com (finance) from St. Xaviers College and 3 Actuarial Papers passed from IFOA and IAI )