To create a frequency distribution table from data, you essentially categorize your data into intervals and count how often each interval appears. Here's a step-by-step guide:
1. Determine the Range of Your Data:
Find the highest and lowest values in your dataset. This gives you the overall range you need to cover.
2. Decide on the Number of Class Intervals (Bins):
- There's no fixed rule, but generally, aim for 5-20 intervals. Fewer intervals can oversimplify the data, while too many can make patterns hard to see.
- Consider the size of your dataset; larger datasets can usually accommodate more intervals.
- Use Sturges' Rule as a guideline: Number of intervals ≈ 1 + 3.322 * log(n), where n is the number of data points. This is just a suggestion, and you may adjust it based on your specific data.
3. Calculate the Class Interval Width:
- Divide the range of your data by the desired number of class intervals. This gives you the approximate width of each interval.
- Round the interval width to a convenient number. It's often best to round up to ensure all data is included.
4. Define the Class Intervals:
- Start with the lowest value in your dataset (or a value slightly lower) as the lower limit of the first interval.
- Add the interval width to the lower limit to get the upper limit of the first interval.
- Repeat this process to define all subsequent intervals. Ensure the intervals are continuous and non-overlapping. For example, if your first interval is 10-19, the next should be 20-29, not 19-28.
5. Tally the Data:
- Go through your dataset and count how many data points fall into each interval. This is the "frequency" for each interval. A tally mark system can be helpful for keeping track (e.g., |||| represents 4, and ||||| represents 5).
6. Create the Frequency Distribution Table:
- Create a table with the following columns:
- Class Interval: List the defined intervals.
- Tally (Optional): Show the tally marks for each interval.
- Frequency: The number of data points in each interval.
- Relative Frequency (Optional): The proportion of data points in each interval (Frequency / Total number of data points). Expressed as a decimal or percentage.
- Cumulative Frequency (Optional): The sum of the frequencies for the current interval and all preceding intervals.
Example:
Let's say you have the following data: 12, 15, 18, 20, 22, 25, 25, 28, 30, 32, 35, 38, 40, 42, 45
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Range: 45 - 12 = 33
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Number of Intervals (Example): 5
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Interval Width: 33 / 5 = 6.6. Round up to 7.
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Class Intervals:
- 12-18
- 19-25
- 26-32
- 33-39
- 40-46
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Tally & Frequency:
Class Interval Tally Frequency 12-18 19-25 26-32 33-39 40-46
This table summarizes how the data is distributed across the different intervals. From this table you can analyze patterns, calculate measures of central tendency, and gain a better understanding of the underlying data.
