Express the mean of the data set shown in the frequency...

Express the mean of the data set shown in the frequency table algebraically.
$$\begin{array}{|c|c|}\hline \text { Price } & {\text { Frequency }} \\ \hline x & {y} \\ \hline \text { w } & {5} \\ \hline 16 & {4} \\ \hline 18 & {v} \\ \hline\end{array}$$

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Key Concepts

Arithmetic Mean

The arithmetic mean is a statistical measure that represents the central value of a dataset. It is calculated by summing all the data values and dividing this total by the number of data points, providing a single value that is representative of the overall data set.

Frequency Distribution

A frequency distribution is a table or chart that displays the frequency (or count) of various outcomes in a dataset. It organizes data in such a way that each unique value or range of values is paired with the number of times it occurs, which is essential for analyzing the distribution of data.

Weighted Average

A weighted average is a technique used to calculate the mean of a dataset where different values contribute differently to the total. In cases where each value has an associated frequency or weight, each value is multiplied by its frequency before summing, and this total is then divided by the sum of the frequencies. This method accurately reflects the impact of each value based on its occurrence.

Algebraic Expression

An algebraic expression uses variables and constants to represent mathematical relationships and operations. It allows the formulation of general expressions for computations, such as the mean in a frequency distribution, which can then be applied to specific instances by substituting the appropriate values.

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