Range Practice Questions

Range is a measure of dispersion that indicates how spread out the values in a dataset are.

Example 1: You are given a dataset of the ages of students in a classroom: 18, 19, 20, 21, 22, 35, 18, 23?

Solution:

Maximum Value = 35

Minimum Value = 18

Range = 35 - 18 = 17

The range of ages among the students is 17 years.

Example 2: You are given a dataset of the heights of students in a classroom (in cm): 150, 155, 160, 165, 170, 175. Find Range.

Solution:

Maximum Value = 175 cm

Minimum Value = 150 cm

Range = 175 - 150 = 25 cm

The range of heights of students is 25 cm

Example 3: Consider a dataset of exam scores for a class: Scores: 85, 92, 78, 96, 64, 89, 75, find the range?

Solution:

Maximum Value = 96

Minimum Value = 64

Range = 96 - 64 = 32

So, the range of the exam scores is 32.

Example 4: Consider a dataset of daily temperature of a city( in °F): 68°F, 72°F, 75°F, 70°F, 74°F. Find temperature range.

Solution:

Maximum Value = 75°F

Minimum Value = 68°F

Range = 75 - 68 = 7°F

Hence the temperature range is 7°F

Example 5: Imagine a dataset of monthly rainfall (in millimeters) for a city for the past year:

Rainfall: 50, 48, 52, 58, 45, 70, 65, 80, 40, 42, 75, 90, find the range of monthly rainfall for the city?

Solution:

Maximum Value = 90

Minimum Value = 40

Range = 90 - 40 = 50

The range of monthly rainfall for the city is 50 mm

Example 6: Consider the following dataset representing the ages of participants in a survey: 22, 28, 34, 31, 25, 30, 29, 33, 27, 24

Calculate the range of the ages in this dataset.

Solution:

Identify the Maximum Value: The highest age in the dataset is 34.

Identify the Minimum Value: The lowest age in the dataset is 22.

Calculate the Range:

Range = Maximum value − Minimum value

Range = Maximum value−Minimum value = 34−22 = 12

Answer: The range of the ages in this dataset is 12 years.

Example 7: Compare and contrast the range with other measures of variability such as variance and standard deviation.

Solution:

• Range: Measures the difference between the maximum and minimum values; it is simple but sensitive to outliers.
• Variance: Measures the average squared deviation of each data point from the mean, providing a more comprehensive understanding of variability, but is more complex to calculate.
• Standard Deviation: The square root of variance, it is also a measure of spread but is in the same units as the data, making it easier to interpret than variance.

Practice Questions

Q1. You have the following test scores of 5 students: 85, 90, 78, 92, 88. Determine the range of the test scores.

Q2. Calculate the range for the following dataset: 12, 15, 20, 25, 30, 35, 40, 45?

Q3. You have a dataset of the heights (in inches) of a group of individuals: 62, 67, 71, 68, 70, 75, 61, 66, 69, 70. Determine the range of heights?

Q4. A survey of 10 people recorded their ages as follows: 25, 32, 28, 45, 34, 50, 29, 41, 33, 36. Calculate the range of the ages.

Q5. Given the following grouped data, calculate the range:

Q6. For the grouped data below, determine the range: