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Frequency Tables
Organizing Data into Counts
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A frequency table is a simple way to organize raw data by showing each value or group and how often it appears. It helps students turn a long, messy list of numbers into a clear summary that is easier to read and analyze. Frequency tables are used in science, business, sports, and social studies whenever people need to describe data. They are often the first step before making graphs or calculating statistics.
To build a frequency table, you list the possible values or class intervals, count how many data points fall into each one, and record those counts as frequencies. You can also add relative frequency to show the proportion or percent of the total in each category. For grouped data, class intervals should be non-overlapping and cover the full range of the data. Once the table is complete, patterns such as clusters, gaps, and the most common values become much easier to see.
Key Facts
- Frequency = number of times a value or class appears in the data set.
- Relative frequency = .
- Percent frequency = (frequency / total) x 100%
- Cumulative frequency = running total of frequencies from top to bottom.
- Class width = upper class limit - lower class limit, if intervals are equally spaced.
- Sum of all frequencies = total number of observations, .
Vocabulary
- Frequency
- Frequency is the count of how many times a particular value or class occurs in a data set.
- Relative frequency
- Relative frequency is the fraction or decimal part of the total data that falls in a given category.
- Cumulative frequency
- Cumulative frequency is the total obtained by adding frequencies up to and including a given row.
- Class interval
- A class interval is a range of values used to group data in a frequency table.
- Raw data
- Raw data is the original unorganized list of observations collected before any sorting or counting.
Common Mistakes to Avoid
- Using overlapping class intervals, which is wrong because one data value could fit into more than one class and create confusion in the counts.
- Forgetting to check that all frequencies add to the total, which is wrong because the table then does not represent the full data set accurately.
- Mixing up frequency and relative frequency, which is wrong because one is a count and the other is a proportion of the whole.
- Choosing class intervals with uneven widths without noting it, which is wrong because it can make comparisons misleading and harder to interpret.
Practice Questions
- 1 A quiz has scores: 5, 7, 5, 8, 6, 7, 5, 9, 6, 7. Make a frequency table for the values 5, 6, 7, 8, and 9, and find the relative frequency of each score.
- 2 The data set is 12, 15, 18, 19, 20, 22, 24, 25, 27, 29, 30, 31. Create grouped classes 10 to 14, 15 to 19, 20 to 24, 25 to 29, and 30 to 34. Find the frequency and cumulative frequency for each class.
- 3 A student says a frequency table is more useful than a raw list because it loses no important information. Explain when this statement is true and when grouping data into classes can hide details.