Mean, median, mode, and range are simple statistics that help describe a set of numbers. They let you summarize many data values with a few useful clues about what is typical and how spread out the data are. For example, the data set 2, 4, 4, 6, 9, 10, 13 can be described by its average value, middle value, most common value, and total spread.
These tools matter because they help you compare test scores, sports statistics, survey results, and measurements clearly.
Key Facts
- Mean = sum of data values ÷ number of data values.
- For 2, 4, 4, 6, 9, 10, 13, mean = 48 ÷ 7 = 6.86.
- Median is the middle value when the data are ordered from least to greatest.
- For 2, 4, 4, 6, 9, 10, 13, median = 6.
- Mode is the value that appears most often, so the mode is 4.
- Range = maximum - minimum, so range = 13 - 2 = 11.
Vocabulary
- Mean
- The mean is the average found by adding all values and dividing by the number of values.
- Median
- The median is the middle value of an ordered data set, or the average of the two middle values if there are an even number of values.
- Mode
- The mode is the value or values that occur most often in a data set.
- Range
- The range is the difference between the greatest and least values in a data set.
- Outlier
- An outlier is a data value that is much higher or lower than most of the other values.
Common Mistakes to Avoid
- Finding the median before ordering the data. The median must be based on values arranged from least to greatest, or the middle position may be wrong.
- Dividing the sum by the wrong number of values when finding the mean. Count every data value, including repeated values, because each one contributes to the average.
- Choosing the largest number as the mode. The mode is the most frequent value, not the biggest value.
- Forgetting that outliers can strongly affect the mean. A very high or low value can pull the mean away from what feels typical, so the median may better represent the center.
Practice Questions
- 1 Find the mean, median, mode, and range of the data set 3, 5, 5, 7, 8, 12.
- 2 A student scored 70, 75, 80, 80, and 95 on five quizzes. Find the mean, median, mode, and range.
- 3 A town compares home prices using both the mean and the median. Explain which measure of center is usually better if a few mansions are much more expensive than the rest, and why.