Range

Lesson

The range is calculated by subtracting the smallest value from the largest value in the dataset. It is a simple measure of dispersion and can be helpful in understanding the spread of data points in a dataset.

Practice Question #1

What is the range of the following dataset: 12, 15, 18, 22, 25, 30?

A) 15

B) 18

C) 20

D) 22

Select an option above to see an explanation here.

A) The range is not 15, as it is not the difference between the largest and smallest values. B) The range is 18 (30 - 12), which is the correct answer. C) The range is not 20, as it is not the difference between the largest and smallest values. D) The range is not 22, as it is not the difference between the largest and smallest values.

Terms

Range:: The difference between a dataset's largest and smallest values.

Practice Question #2

Which of the following is NOT a measure of dispersion?

A) Range

B) Standard Deviation

C) Mean

D) Interquartile Range

Select an option above to see an explanation here.

A) Range is a measure of dispersion. B) Standard Deviation is a measure of dispersion. C) Mean is a measure of central tendency, not dispersion, making it the correct answer. D) Interquartile Range is a measure of dispersion.

Do Not Confuse With

Standard Deviation:: A measure of dispersion that considers the average distance of each data point from the mean.
Mean:: The average value of a dataset is calculated by adding all data points and dividing by the number of data points.
Median:: The middle value of a dataset when the data points are arranged in ascending or descending order.

Practice Question #3

If the minimum value in a dataset is 10 and the maximum value is 50, what is the range?

A) 30

B) 40

C) 50

D) 60

Select an option above to see an explanation here.

A) The range is not 30, as it is not the difference between the largest and smallest values. B) The range is 40 (50 - 10), which is the correct answer. C) The range is not 50, as it is not the difference between the largest and smallest values. D) The range is not 60, as it is not the difference between the largest and smallest values.

Historical Example

In the early 1900s, a study was conducted to analyze the heights of a large group of people. The researchers found that the range of heights was 24 inches, with the shortest person being 60 inches tall and the tallest person being 84 inches tall. This range helped the researchers understand the dispersion of heights within the population.

Practice Question #4

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Formulas to Remember

Range = Maximum Value - Minimum Value

Practice Question #5

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Formula Examples

Suppose we have the following dataset of stock prices: $50, $55, $60, $65, $70. We need to find the maximum and minimum values and subtract them to calculate the range. 1. maximum value: $70 2. minimum value: $50 3. range: $70 - $50 = $20

Practice Question #6

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Pitfalls to Remember

Small sample size:: The range may not accurately represent the dispersion of a dataset if the sample size is too small.
Outliers:: The range is sensitive to outliers, which can significantly affect the result and may not accurately represent the dispersion of the data.