A random sample of 30 states shows the number of specialty...

A random sample of 30 states shows the number of specialty coffee shops for a specific company. Find the mean and modal class for the data. Class boundaries $\quad$ Frequency $\begin{array}{ccc}{0.5-19.5} & {12} \\ {19.5-38.5} & {7} \\ {38.5-57.5} & {5} & {} \\ {57.5-76.5} & {3} & \\ {76.5-95.5} & {3}\end{array}$

A random sample of 30 states shows the number of specialty coffee shops for a specific company. Find the mean and modal class for the data.
Class boundaries $\quad$ Frequency
$\begin{array}{ccc}{0.5-19.5} & {12} \\ {19.5-38.5} & {7} \\ {38.5-57.5} & {5} & {} \\ {57.5-76.5} & {3} & \\ {76.5-95.5} & {3}\end{array}$

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Key Concepts

Grouped Data

Grouped data refers to data that have been organized into intervals or classes, making it easier to analyze large data sets. In this approach, the individual data values are not shown; instead, frequencies are provided for ranges or intervals of data.

Mean of Grouped Data

The mean of grouped data is calculated by approximating each class interval's contribution using its midpoint. Each class midpoint is multiplied by its corresponding frequency, and the sum of these products is then divided by the total frequency, providing an estimate of the overall average. This method is used because the exact values within each group are not available.

Modal Class

The modal class is the class interval that has the highest frequency in a grouped frequency distribution. It identifies the range in which the most data points fall, providing insight into the most common values within the data set.

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