Introduction
Understanding mean, mode, median, and range is essential for anyone studying basic statistics. This mean mode median range worksheet with answers provides a practical way to practice calculating these measures, reinforce learning, and check comprehension instantly. By working through the exercises, learners can build confidence and see how each statistic summarizes a data set in a different yet complementary way.
Understanding the Four Measures
What is Mean?
The mean (average) is calculated by adding all values together and dividing by the number of values.
[ \text{Mean} = \frac{\sum \text{values}}{n} ]
Key point: The mean is sensitive to extreme values (outliers) Small thing, real impact..
What is Mode?
The mode is the value that appears most frequently in a data set. A set may have one mode, multiple modes, or no mode at all.
Key point: Mode is especially useful for categorical data where numerical averaging is not meaningful Easy to understand, harder to ignore. Nothing fancy..
What is Median?
The median is the middle value when the data are arranged in ascending order. If the number of observations is even, the median is the average of the two central numbers The details matter here. Still holds up..
Key point: The median represents the center of a data set and is resistant to outliers.
What is Range?
The range is the difference between the highest and lowest values.
[ \text{Range} = \text{Maximum value} - \text{Minimum value} ]
Key point: Range gives a quick sense of data spread but can be misleading with extreme values.
How to Use a Worksheet Effectively
- Read each question carefully – identify the data set and what is being asked.
- Organize the data – write the numbers in order for median calculation.
- Calculate each measure – follow the formulas shown above.
- Check your answers – compare with the answer key provided in this article.
- Reflect on differences – notice how the mean, median, and mode may differ, especially with skewed data.
Sample Worksheet with Answers
Below are five data sets. For each, determine the mean, mode, median, and range. The answers are provided in bold after each question Most people skip this — try not to..
Data Set A
5, 7, 9, 10, 10, 12
- Mean: 5 + 7 + 9 + 10 + 10 + 12 = 53; 53 ÷ 6 ≈ 8.83
- Mode: 10 (appears twice)
- Median: Ordered set = 5, 7, 9, 10, 10, 12 → middle values are 9 and 10; (9 + 10) ÷ 2 = 9.5
- Range: 12 − 5 = 7
Data Set B
3, 4, 4, 5, 8, 8, 8
- Mean: (3 + 4 + 4 + 5 + 8 + 8 + 8) = 40; 40 ÷ 7 ≈ 5.71
- Mode: 8 (appears three times)
- Median: Ordered set = 3, 4, 4, 5, 8, 8, 8 → middle value is 5
- Range: 8 − 3 = 5
Data Set C
2, 2, 4, 6, 8, 10
- Mean: (2 + 2 + 4 + 6 + 8 + 10) = 32; 32 ÷ 6 ≈ 5.33
- Mode: 2 (appears twice)
- Median: Ordered set = 2, 2, 4, 6, 8, 10 → middle values are 4 and 6; (4 + 6) ÷ 2 = 5
- Range: 10 − 2 = 8
Data Set D
15, 15, 15, 15
- Mean: (15 × 4) ÷ 4 = 15
- Mode: 15 (all values are the same)
- Median: Ordered set = 15, 15, 15, 15 → middle values are 15 and 15; average = 15
- Range: 15 − 15 = 0
Data Set E
1, 2, 3, 4, 5, 6, 7, 8
- Mean: (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8) = 36; 36 ÷ 8 = 4.5
- Mode:
