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The range in a frequency distribution table gives a quick picture of how data is spread out. To calculate the range, you subtract the smallest data value from the largest data value. It's a straightforward measure that helps you understand the span of your data. For example, if the smallest number in your data set is 143 and the largest is 153, the range is \[ \text{Range} = 153 - 143 = 10\] The range doesn't provide any information on the distribution of data between the extreme values, but it's an essential first step. Knowing the range helps you set up your class intervals, which is crucial for organizing and analyzing your data effectively.

Class intervals are the ranges you set to group your data. They make it easier to analyze and interpret. To create class intervals, you use the range calculated earlier. The class interval size, or class width, is found by dividing the range by the desired number of classes. For example, to have five classes:\[ \text{Class Width} = \left\lceil \frac{10}{5} \right\rceil = 2\] Rounded up to the nearest whole number, this ensures that your intervals capture all the data points without overlap.
Starting with the smallest data point, 143, you define each class interval by adding the class width to create successive ranges like 143-145 and so on.

• 143 - 145
• 146 - 148
• 149 - 151
• 152 - 154

This step is vital for structuring a well-organized frequency distribution table.

A frequency distribution table aids in simplifying data analysis. It helps visualize the data to see patterns and trends. By tallying how many data points fall into each class interval, you can quickly discern where data concentrations are.
For instance:

• 143 - 145: 4 data points
• 146 - 148: 8 data points
• 149 - 151: 6 data points
• 152 - 154: 2 data points

The table shows that most of the car's range data is concentrated within 146-148 miles. This overview is helpful in identifying how test results in different categories compare to one another in terms of frequency.
It reduces large volumes of data into a format that is easier to interpret and analyze, especially useful in spotting characteristics and tendencies that might not be obvious from raw numbers alone.

Frequency distribution tables play a significant role in mathematics education. They provide a hands-on approach to learning concepts like data organization, statistical analysis, and mathematical reasoning skills.
These tables are practical tools for:

• standing as a first introduction to the world of statistics
• showing real-world applications of mathematical calculations
• developing analytical and critical-thinking skills

Working through an exercise to develop a frequency distribution table involves several steps that mirror real-world problem-solving. Students learn to calculate, organize, and analyze data—key skills that are transferable to many fields and everyday decision-making.
Additionally, understanding the connection between mathematical theory and application improves engagement and retention, fostering a deeper appreciation for mathematics.