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The range is the simplest measure of dispersion and is calculated as the difference between the maximum and minimum values in a dataset.
It gives a quick sense of the spread of values but can be heavily influenced by outliers.
Formula: Range = Maximum value − Minimum value
1. Range in a Discrete Series
Discrete data consist of distinct, separate values, often counted data.
Example:
Imagine we're looking at the number of prescriptions filled by a pharmacy each day over a week. The data might look like this:
Calculating Range:
Identify the maximum value: In this case, 60 on Saturday.
Identify the minimum value: 40 on Wednesday.
Subtract the minimum value from the maximum value to find the range: 60−40=20.
So, the range of prescriptions filled in a day is 20, indicating the difference between the busiest and slowest days.
2. Range in a Continuous Series
Continuous data are data points that can take any value within a range, and they are often grouped into intervals for analysis.
Example:
Consider a clinical trial where we're measuring the reduction in blood pressure (in mmHg) of patients using a new medication.
The data might be grouped as follows:
For continuous data, the range is calculated based on the intervals, but the exact minimum and maximum values within those intervals aren't always known.
However, you can approximate the range using the boundaries of the intervals.
Calculating Range:
Identify the interval containing the maximum value: The 50-59 mmHg interval.
Identify the interval containing the minimum value: The 10-19 mmHg interval.
Since the exact values aren't known, use the interval boundaries to approximate the range. For a more precise estimate, you might use the midpoint of the intervals, but for the range, the boundaries give a quick estimate.
Assuming the minimum possible reduction is 10 mmHg, and the maximum possible reduction is 59 mmHg (the boundaries of our intervals), the approximate range is 59−10=4959−10=49 mmHg.
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