Maximum Wind Speeds The data show the maximum wind speeds in...

Maximum Wind Speeds The data show the maximum wind speeds in miles per hour recorded for 40 states. Construct a frequency distribution using 7 classes. $$ \begin{array}{ccccc}{59} & {78} & {62} & {72} & {67} \\ {76} & {92} & {77} & {64} & {83} \\ {64} & {70} & {67} & {75} & {75} \\ {78} & {75} & {71} & {72} & {93} \\ {68} & {69} & {76} & {72} & {85} \\ {64} & {70} & {77} & {74} & {72} \\ {53} & {67} & {48} & {76} & {59} \\ {87} & {53} & {77} & {70} & {63}\end{array} $$

Maximum Wind Speeds The data show the maximum
wind speeds in miles per hour recorded for 40 states.
Construct a frequency distribution using 7 classes.
$$
\begin{array}{ccccc}{59} & {78} & {62} & {72} & {67} \\ {76} & {92} & {77} & {64} & {83} \\ {64} & {70} & {67} & {75} & {75} \\ {78} & {75} & {71} & {72} & {93} \\ {68} & {69} & {76} & {72} & {85} \\ {64} & {70} & {77} & {74} & {72} \\ {53} & {67} & {48} & {76} & {59} \\ {87} & {53} & {77} & {70} & {63}\end{array}
$$

Key Concepts

Data Grouping

Data grouping involves organizing raw data into classes to facilitate a clearer overview and interpretation. Grouping data into classes transforms a large and potentially unwieldy data set into a more manageable form, allowing for easier identification of trends, central tendencies, and variability.

Determining Range

The range is the difference between the maximum and minimum values in a data set. In the context of constructing a frequency distribution, determining the range is the first step, as it enables us to understand the spread of the data, which in turn assists in deciding an appropriate class width.

Class Width Calculation

Class width is calculated by dividing the range of the data set by the desired number of classes. This value indicates the size of each interval and is used to ensure that the classes are of equal width, which can simplify the interpretation and comparison of frequencies across classes.

Frequency Distribution

A frequency distribution is a summary that shows the number of observations (or frequency) that fall within specific intervals, known as classes, for a given data set. This tool is essential in statistics for organizing and summarizing large sets of data to reveal patterns such as the distribution of values and central trends.

Class Intervals (Classes)

Class intervals are the grouped ranges into which data points are organized in a frequency distribution. By dividing the entire range of data into a series of non-overlapping groups, one can more easily analyze the structure of the data. The selection of these intervals has a significant effect on the interpretation of the distribution.

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