Do the following: a. Compute the sample variance. b....

Do the following: a. Compute the sample variance. b. Determine the sample standard deviation. A consumer watchdog organization is concerned about credit card debt. A survey of 10 young adults with credit card debt of more than $\$ 2,000$ showed they paid an average of just over $\$ 100$ per month against their balances. Listed below are the amounts each young adult paid last month. $$ \begin{array}{llllllllll} \hline 110 & \$ 126 & \$ 103 & \$ 93 & \$ 99 & \$ 113 & \$ 87 & \$ 101 & \$ 109 & \$ 100 \\ \hline \end{array} $$

Do the following:
a. Compute the sample variance.
b. Determine the sample standard deviation.
A consumer watchdog organization is concerned about credit card debt. A survey of 10 young adults with credit card debt of more than $\$ 2,000$ showed they paid an average of just over $\$ 100$ per month against their balances. Listed below are the amounts each young adult paid last month.
$$
\begin{array}{llllllllll}
\hline 110 & \$ 126 & \$ 103 & \$ 93 & \$ 99 & \$ 113 & \$ 87 & \$ 101 & \$ 109 & \$ 100 \\
\hline
\end{array}
$$

Key Concepts

Degrees of Freedom (Bessel's Correction)

Degrees of freedom, used in the calculation of sample variance, represent the number of independent values that can vary in an analysis without breaking any constraints. When calculating variance from a sample, replacing n with n-1 (Bessel's correction) compensates for the bias in the estimation of the population variance, providing a more accurate measure.

Sample Standard Deviation

The sample standard deviation is the positive square root of the sample variance and is used to measure the spread of data in the same units as the original measurements. It offers an easy-to-interpret metric that indicates how much, on average, the observations differ from the sample mean.

Sample Variance

The sample variance quantifies the dispersion of the data points around the sample mean. It is computed by taking the sum of the squared differences between each observation and the sample mean, and then dividing this sum by the degrees of freedom, which is the number of observations minus one (n-1). This adjustment, known as Bessel's correction, provides an unbiased estimator of the population variance.

Sample Mean

The sample mean is the average of the values in the sample and serves as a measure of central tendency. It is calculated by summing all the sample values and then dividing by the number of observations. The mean provides a reference point for measuring deviations of individual data points, which is crucial when calculating variance and standard deviation.

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