Constructing a Frequency Distribution and a Relative Frequency Histogram In Exercises 37–40, construct a frequency distribution and a relative frequency histogram for the data set using five classes. Which class has the greatest relative frequency and which has the least relative frequency?
Taste Test
Data set: Ratings from 1 (lowest) to 10 (highest) provided by 36 people after taste-testing a new flavor of protein bar 2 6 9 2 9 9 6 10 5 8 7 6 5 10 1 4 9 3 4 5 3 6 5 2 4 9 2 9 3 3 6 5 1 9 4 2

Verified step by step guidance

1. Step 1: Determine the range of the data by subtracting the smallest value (1) from the largest value (10). This will help in determining the class width.
2. Step 2: Calculate the class width by dividing the range by the number of classes (5). Round up to the nearest whole number if necessary to ensure all data points are included.
3. Step 3: Define the class intervals. Start with the smallest value in the data set as the lower limit of the first class, and add the class width to determine the upper limit of each class. Repeat this process to create five non-overlapping classes.
4. Step 4: Construct the frequency distribution by counting how many data points fall into each class interval. Record these frequencies in a table.
5. Step 5: Calculate the relative frequency for each class by dividing the frequency of each class by the total number of data points (36). Then, use the relative frequencies to construct a relative frequency histogram, ensuring the x-axis represents the class intervals and the y-axis represents the relative frequencies.

Key Concepts

Frequency Distribution

A frequency distribution is a summary of how often each value occurs in a dataset. It organizes data into classes or intervals, showing the number of observations (frequency) that fall within each class. This helps in understanding the distribution of data points and identifying patterns or trends within the dataset.

Relative Frequency

Relative frequency is the ratio of the frequency of a particular class to the total number of observations in the dataset. It provides a way to express how common or rare a class is relative to the entire dataset, often represented as a percentage. This concept is crucial for comparing classes and understanding their significance in the context of the whole data set.

Histogram

A histogram is a graphical representation of the frequency distribution of a dataset. It consists of bars that represent the frequency of data points within specified intervals (classes). The height of each bar indicates the frequency, allowing for a visual comparison of the distribution and helping to identify which classes have the greatest and least relative frequencies.