These data represent the net worth (in millions of dollars)...

These data represent the net worth (in millions of dollars) of 45 national corporations. Find the mean and modal class for the data. Class limits $\quad$ Frequency $\begin{array}{lc}{10-20} & {2} \\ {21-31} & {8} \\ {32-42} & {15} \\ {43-53} & {7} \\ {54-64} & {10} \\ {65-75} & {3}\end{array}$

These data represent the net worth (in millions of dollars) of 45 national corporations. Find the mean and modal class for the data.
Class limits $\quad$ Frequency
$\begin{array}{lc}{10-20} & {2} \\ {21-31} & {8} \\ {32-42} & {15} \\ {43-53} & {7} \\ {54-64} & {10} \\ {65-75} & {3}\end{array}$

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Key Concepts

Grouped Data

Grouped data is used when individual data points are organized into intervals or classes, along with a corresponding frequency count for each interval. This method simplifies large sets of data by summarizing them into manageable groups, making it easier to analyze overall patterns and trends.

Frequency Distribution

A frequency distribution organizes data in terms of the number of observations falling within each class interval. It provides a clear overview of how often each range of values occurs in a dataset, which is essential for calculating various descriptive statistics.

Mean of Grouped Data

The mean of grouped data is an estimate of the central value of the dataset. It is calculated by multiplying the midpoint of each class interval by its corresponding frequency, summing these products, and then dividing by the total frequency. This weighted average technique accounts for the distribution of observations across the intervals.

Modal Class

The modal class is the class interval that has the highest frequency within a frequency distribution. It represents the group of values that occurs most frequently in the dataset and provides insight into the most common range of data values.

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