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.


Earthquake Depths Use the depths (km) of the 600 earthquakes included in Data Set 24 “Earthquakes.” Use a class width of 10.0 km and begin with a lower class limit of 0.0 km. 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 depths of 600 earthquakes using a class width of 10.0 km, starting with a lower class limit of 0.0 km. 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 0.0 km and add the class width of 10.0 km to create successive intervals. For example, the first interval will be 0.0–10.0 km, the second will be 10.0–20.0 km, and so on. Continue this process until you cover the range of the data.
3. Step 3: Count the frequencies. For each class interval, count the number of earthquake depths that fall within that range. This can be done using technology such as Excel, a statistical calculator, or statistical software. Record the frequencies for each class interval.
4. Step 4: Construct the frequency distribution table. Create a table with two columns: one for the class intervals and one for the corresponding frequencies. Populate the table with the intervals and their respective frequencies from Step 3.
5. Step 5: Assess normality. To determine if the frequency distribution appears to be a normal distribution, plot a histogram of the data using the class intervals and frequencies. A normal distribution will typically have a bell-shaped curve, with frequencies increasing to a peak in the middle and then symmetrically decreasing. Analyze the shape of the histogram to make your assessment.

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 visualizing the distribution of data points and identifying patterns, such as skewness or modality.

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. In this case, a class width of 10.0 km means each class will encompass a range of 10 kilometers, which helps in grouping the earthquake depths effectively for analysis.

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. To determine if the frequency distribution of earthquake depths is normal, one would look for symmetry and the presence of a single peak in the distribution.