This frequency distribution represents the commission earned...

This frequency distribution represents the commission earned (in dollars) by 100 salespeople employed at several branches of a large chain store. Find the mean and modal class for the data. Class limits $\quad$ Frequency $\begin{array}{lc}{150-158} & {5} \\ {159-167} & {16} \\ {168-176} & {20} \\ {177-185} & {21} \\ {186-194} & {20} \\ {195-203} & {15} \\ {204-212} & {3}\end{array}$

This frequency distribution represents the commission earned (in dollars) by 100 salespeople employed at several branches of a large chain store. Find the mean and modal class for the data.
Class limits $\quad$ Frequency
$\begin{array}{lc}{150-158} & {5} \\ {159-167} & {16} \\ {168-176} & {20} \\ {177-185} & {21} \\ {186-194} & {20} \\ {195-203} & {15} \\ {204-212} & {3}\end{array}$

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Key Concepts

Modal Class

The modal class is the class interval within a frequency distribution that has the highest frequency, meaning it contains the greatest number of observations. Identifying the modal class helps indicate the range in which the most typical or common values occur in a data set.

Mean of Grouped Data

The mean of grouped data is an estimate of the central tendency that is calculated by multiplying the midpoint of each class interval by its corresponding frequency, summing these products, and then dividing by the total number of observations. This method provides an approximation of the average value when raw data are not individually available.

Grouped Data

Grouped data is information that has been organized into intervals or classes, rather than listed as individual data points. This categorization is typically used when dealing with a large span of values, and it facilitates the calculation of key statistical measures such as the mean and modality.

Frequency Distribution

A frequency distribution is a tabular representation that displays the number of observations within different intervals or classes in a data set. It helps in summarizing large data sets by organizing data into categories, which makes it easier to observe patterns and trends.

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