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.
Systolic Blood Pressure Use the systolic blood pressures of the 300 subjects included in Data Set 1 “Body Data.” Use a class width of 20 mm Hg and begin with a lower class limit of 80 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 systolic blood pressures of 300 subjects using a class width of 20 mm Hg, starting with a lower class limit of 80 mm Hg. Additionally, you need to assess whether the resulting distribution appears to be a normal distribution.
2. Step 2: Define the class intervals. Start with the lower class limit of 80 mm Hg and add the class width (20 mm Hg) to determine the upper limit of the first class. Continue this process to create subsequent class intervals until all data values are covered. For example, the first class would be 80–99 mm Hg, the second class 100–119 mm Hg, and so on.
3. Step 3: Tally the data. Using the provided data set (downloaded from TriolaStats.com), count the number of data points (frequencies) that fall within each class interval. This can be done using statistical software or a spreadsheet program.
4. Step 4: Construct the frequency distribution table. Create a table with columns for the class intervals, frequencies, and possibly relative frequencies (frequencies divided by the total number of data points). This table will summarize the distribution of the data.
5. Step 5: Assess normality. Plot the frequency distribution as a histogram. A normal distribution typically appears as a symmetric, bell-shaped curve. Evaluate the shape of the histogram to determine if it resembles a normal distribution. Additionally, you can calculate measures like skewness or use statistical tests (e.g., Shapiro-Wilk test) to assess normality more formally.

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.