Exercises 29–34 involve large sets of data, so technology should be used. Complete lists of the data are not listed in Appendix B, but they can be downloaded from the website TriolaStats.com. Use the indicated data and construct the frequency distribution.


Diastolic Blood Pressure Use the diastolic blood pressures of the 300 subjects included in Data Set 1 “Body Data.” Use a class width of 15 mm Hg and begin with a lower class limit of 40 mm Hg. Does the frequency distribution appear to be a normal distribution?

Verified step by step guidance

1. Step 1: Understand the problem. You are tasked with constructing a frequency distribution for the diastolic blood pressures of 300 subjects. The class width is given as 15 mm Hg, and the starting lower class limit is 40 mm Hg. Additionally, you need to assess whether the resulting frequency distribution resembles a normal distribution.
2. Step 2: Define the class intervals. Start with the lower class limit of 40 mm Hg. Add the class width (15 mm Hg) successively to determine the upper limit of each class and the lower limit of the next class. For example, the first class would be 40–54 mm Hg, the second class would be 55–69 mm Hg, and so on. Continue this process until all data values are covered.
3. Step 3: Tally the data. Using the diastolic blood pressure data from Data Set 1, count how many data points fall into each class interval. This will give you the frequency for each class. Use technology (e.g., Excel, statistical software, or a graphing calculator) to efficiently sort and count the data.
4. Step 4: Construct the frequency distribution table. Create a table with three columns: Class Interval, Frequency, and Relative Frequency (optional). Fill in the class intervals and their corresponding frequencies. If desired, calculate the relative frequency for each class by dividing the frequency of the class by the total number of data points (300).
5. Step 5: Assess normality. Plot the frequency distribution as a histogram. Check if the histogram has a bell-shaped curve, which is characteristic of a normal distribution. Look for symmetry around the center and tapering tails. If the distribution is approximately symmetric and bell-shaped, it may resemble a normal distribution.

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 within each class. This helps in visualizing the distribution of data points and identifying patterns, such as skewness or modality, which are essential for further statistical analysis.

Class Width

Class width refers to the range of values that each class in a frequency distribution covers. It is calculated by subtracting the lower limit of a class from its upper limit. Choosing an appropriate class width is crucial, as it affects the granularity of the data representation and can influence the interpretation of the distribution's shape.

Normal Distribution

A normal distribution is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean. It is characterized by its bell-shaped curve. Identifying whether a frequency distribution approximates a normal distribution is important for applying various statistical methods and tests that assume normality.