The ages of all of the students in a science class are shown...

The ages of all of the students in a science class are shown in the table. Find the variance and the standard deviation.
$\begin{array}{|c|c|}\hline \text { Age } & {\text { Frequency }} \\ \hline 18 & {1} \\ {17} & {2} \\ {16} & {9} \\ {15} & {9} \\ \hline\end{array}$

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Key Concepts

Variance

Variance is a statistical measure that quantifies the spread of a data set by calculating the average of the squared differences between each data point and the mean. It provides an indication of how far the values in the set are from the average value.

Standard Deviation

Standard deviation is the square root of the variance and offers a measure of dispersion in the same units as the original data. It indicates the typical distance between each data point and the mean, making it easier to understand the spread of the data.

Mean (Average)

The mean is the sum of all data points divided by the number of data points, representing a central value for the dataset. It serves as a reference point for calculating the variance and standard deviation, especially when data is given in a frequency distribution.

Frequency Distribution

A frequency distribution summarizes how often each value occurs within a dataset. When statistical calculations such as mean, variance, and standard deviation are needed, the frequency of each value is used to weight those values appropriately in the computations.

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