How to Finding Mean, Median, Mode, and Range: Interpreting Charts

Mean, median, mode, and range are the four fundamental measures of a data set. They appear on the GED Math test in the form of word problems, frequency tables, and charts. Knowing how to calculate each measure and interpret what it tells you about a data set will help you tackle statistics questions with confidence.

What Are Mean, Median, Mode, and Range?

These four statistics describe the center and spread of a data set:

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• Mean — the average; add all values and divide by the count
• Median — the middle value when the data is sorted in order
• Mode — the value that appears most often (a set can have no mode, one mode, or multiple modes)
• Range — the spread; subtract the smallest value from the largest

How to Calculate Each Measure

Mean

\(\color{blue}{\text{ Mean } = (\text{ sum of all values }) \div (\text{ number of values })}\)

Example: {4, 8, 6, 5, 7} → \(\color{blue}{\text{ Sum } = 30}\), \(\color{blue}{\text{ Count } = 5}\); \(\color{blue}{\text{ Mean } = 30 \div 5}\) = 6

Median

1. Sort the data from least to greatest.
2. If odd number of values, the median is the middle value.
3. If even number of values, the median is the average of the two middle values.

Example (odd): {3, 5, 7, 9, 11} → Median = 7
Example (even): {3, 5, 7, 9} → \(\color{blue}{\text{ Median } = (5 + 7) \div 2}\) = 6

Mode

The value(s) that appear most frequently. If all values appear once, there is no mode.

Example: {2, 4, 4, 6, 8} → Mode = 4

Range

\(\color{blue}{\text{ Range } = \text{ Maximum }}\) \(\color{blue}{\text{ value } – \text{ Minimum }}\) value

Example: {14, 17, 40, 48, 73, 84, 90} → \(\color{blue}{\text{ Range } = 90 – 14}\) = 76

Step-by-Step Summary

1. List the data values in order from least to greatest.
2. Mean: add all \(\color{blue}{\text{ values } \div \text{ count }}\).
3. Median: find the middle value (or average of the two middle values for even-count sets).
4. Mode: find the value(s) appearing most often.
5. Range: \(\color{blue}{\text{ max } – \text{ min }}\).

Watch: Mean, Median, Mode, and Range (Video Lesson)

Math with Mr. J covers all four measures in a single, clear lesson:

Worked Examples

Example 1: Find the mean, median, mode, and range of: 73, 14, 84, 48, 90, 40, 17.

Sorted: 14, 17, 40, 48, 73, 84, 90
\(\color{blue}{\text{ Mean } = (14+17+40+48+73+84+90) \div 7 = 366 \div 7}\) ≈ 52.3
Median = 48 (4th of 7 values)
Mode = none (all values appear once)
\(\color{blue}{\text{ Range } = 90 – 14}\) = 76

Example 2: Find the mean, median, mode, and range of: 5, 3, 8, 3, 9, 3, 7, 6.

Sorted: 3, 3, 3, 5, 6, 7, 8, 9
\(\color{blue}{\text{ Mean } = (3+3+3+5+6+7+8+9) \div 8 = 44 \div 8}\) = 5.5
\(\color{blue}{\text{ Median } = (5 + 6) \div 2}\) = 5.5
Mode = 3 (appears 3 times)
\(\color{blue}{\text{ Range } = 9 – 3}\) = 6

Example 3: A chart shows test scores: 82, 91, 78, 91, 85. Find the mode and range.

Mode = 91; \(\color{blue}{\text{ Range } = 91 – 78}\) = 13

Example 4: The monthly temperatures (°F) for four months are: 55, 68, 72, 61. Find the mean temperature.

\(\color{blue}{\text{ Mean } = (55+68+72+61) \div 4 = 256 \div 4}\) = 64°F

More Practice: Finding Mean, Median, and Mode (Video)

This Math with Mr. J video reinforces the calculation steps with additional data sets:

Exercises

1. Find the mean of: 12, 8, 15, 20, 5.
2. Find the median of: 3, 11, 7, 2, 9, 5.
3. Find the mode of: 4, 7, 4, 2, 7, 4, 9.
4. Find the range of: 56, 43, 78, 21, 65, 90.
5. A student scored 72, 85, 91, 68, 85 on five tests. Find the mean, median, mode, and range.
6. A frequency chart shows: Score 10 appears 3 times; Score 8 appears 2 times; Score 6 appears 1 time. Find the mean of all 6 scores.

Answers

1. \(\color{blue}{(12+8+15+20+5) \div 5 = 60 \div 5}\) = 12
2. Sorted: 2,3,5,7,9,11; \(\color{blue}{\text{ Median } = (5+7)\div 2}\) = 6
3. 4 (appears 3 times)
4. \(\color{blue}{90 – 21}\) = 69
5. Sorted: 68,72,85,85,91; \(\color{blue}{\text{ Mean }=401\div 5}\)=80.2; Median=85; Mode=85; \(\color{blue}{\text{ Range }=91-68}\)=23
6. \(\color{blue}{(10+10+10+8+8+6)\div 6 = 52\div 6}\) ≈ 8.67

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Frequently Asked Questions

Which measure is most affected by outliers?

The mean is most sensitive to outliers (extreme values), because every data point is included in the sum. The median and mode are more resistant to outliers. That’s why median income is often used instead of mean income.

Can there be more than one mode?

Yes. A data set with two values that both appear most often is called bimodal. If no value repeats, the data set has no mode.

How does range differ from interquartile range?

\(\color{blue}{\text{ Range } = \text{ max } – \text{ min }}\) and describes the full spread. The interquartile range \(\color{blue}{(\text{ IQR }) = Q3 – Q1}\) and describes the middle 50% of the data, making it more resistant to outliers.

Related Topics

• How to Identify an Outlier
• Finding Range, Quartile, and Interquartile Range
• Line Plot
• How to Solve the Frequency Distribution Table
• Distributions in Line Plot