2. Describing Data with Tables and Graphs
Frequency Distributions
3:38 minutesProblem 2.q.4
Textbook Question
Tornado Alley Construct the relative frequency distribution corresponding to the frequency distribution in Exercise 1
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Step 1: Calculate the total frequency by summing all the frequencies provided in the table. Add the values: 3 + 18 + 21 + 15 + 6 + 5 + 0 + 1.
Step 2: For each class interval, divide the frequency of that interval by the total frequency calculated in Step 1. This will give the relative frequency for each interval.
Step 3: Express the relative frequency as a decimal or percentage. For example, if the relative frequency for a class interval is 0.1, you can also express it as 10%.
Step 4: Construct a new table with the same class intervals as the original table, but replace the frequency column with the relative frequency values calculated in Step 2.
Step 5: Verify that the sum of all relative frequencies equals 1 (or 100% if expressed as percentages). This ensures the relative frequency distribution is correctly constructed.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Relative Frequency Distribution
A relative frequency distribution shows the proportion of observations within each category relative to the total number of observations. It is calculated by dividing the frequency of each category by the total frequency. This distribution helps in understanding the likelihood of occurrences within specified ranges, making it easier to compare different categories.
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Frequency Distribution
A frequency distribution is a summary of how often each value occurs in a dataset. It lists the categories of data and their corresponding counts, providing a clear view of the data's distribution. In the context of tornado occurrences, it shows how many years fall into each range of annual tornado counts, which is essential for analyzing trends and patterns.
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Cumulative Frequency
Cumulative frequency is the running total of frequencies through the categories of a frequency distribution. It indicates the number of observations that fall below a particular value. This concept is useful for understanding the overall distribution of data and can help in determining percentiles and other statistical measures.
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