In Exercises 1 and 2, use the data set, which represents the overall average class sizes for 20 national universities. (Adapted from Public University Honors)
37 34 42 44 39 40 41 51 49 31
52 26 31 40 30 27 36 43 48 35


Construct a relative frequency histogram using the frequency distribution in Exercise 1. Then determine which class has the greatest relative frequency and which has the least relative frequency.

Verified step by step guidance

1. Step 1: Organize the data into a frequency distribution. Divide the range of the data into equal intervals (classes) and count how many data points fall into each interval. For example, if the data ranges from 26 to 52, you might create intervals like 25-30, 31-35, 36-40, etc.
2. Step 2: Calculate the relative frequency for each class. Relative frequency is the proportion of data points in each class compared to the total number of data points. Use the formula: $\frac{f}{n}$, where $f$ is the frequency of the class and $n$ is the total number of data points.
3. Step 3: Construct the relative frequency histogram. On the x-axis, plot the class intervals, and on the y-axis, plot the relative frequencies. Each bar's height should correspond to the relative frequency of the class it represents.
4. Step 4: Identify the class with the greatest relative frequency. Look for the tallest bar in the histogram, as it represents the class with the highest proportion of data points.
5. Step 5: Identify the class with the least relative frequency. Look for the shortest bar in the histogram, as it represents the class with the lowest proportion of data points.

Key Concepts

Relative Frequency

Relative frequency is the ratio of the frequency of a particular class to the total number of observations. It provides a way to understand the proportion of data points that fall within a specific category, allowing for comparisons across different classes. This concept is essential for constructing histograms and interpreting the distribution of data.

Histogram

A histogram is a graphical representation of the distribution of numerical data, where the data is divided into intervals (or bins) and the frequency of data points within each interval is represented by the height of bars. It visually summarizes the data set, making it easier to identify patterns, such as the most and least common class sizes in this case.

Frequency Distribution

A frequency distribution is a summary of how often each value occurs in a data set. It organizes the data into classes or intervals and counts the number of observations in each class. Understanding frequency distributions is crucial for creating histograms and analyzing the data's overall structure, including identifying which classes have the highest and lowest relative frequencies.