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

How to finding mean, median, mode, and range: interpreting charts, step by step: the rule in plain language, solved examples worked one line at a time, and practice questions so you can try it yourself before moving on.

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 }=401div 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 = 52div 6}) ≈ 8.67

Frequently Asked Questions

How do you calculate the mean, median, mode, and range?

Use one data set for all four. For 3, 7, 7, 9, 14: the mean is the sum divided by the count, 40 ÷ 5 = 8. The median is the middle value once sorted, 7. The mode is the most frequent value, also 7. The range is largest minus smallest, 14 − 3 = 11. Always sort first, since the median and range depend on order.

How do you interpret mean and median?

Both describe a typical value, but they react differently to extreme values. The mean uses every number, so one very large or small value pulls it. The median only depends on the middle. If five workers earn $30k, $32k, $35k, $36k, and $200k, the mean is $66.6k but the median is $35k, which better describes most of the group. A mean well above the median signals right-skewed data.

How do you find mean, median, mode, and range using a bar graph?

Read the height of each bar to get the values, list them, then calculate. Suppose a bar graph shows books read by five students: 4, 6, 2, 6, 7. Sorted: 2, 4, 6, 6, 7. Mean = 25 ÷ 5 = 5, median = 6, mode = 6 (the two tallest bars match), and range = 7 − 2 = 5. Check the scale on the vertical axis before reading any bar.

How do you find mean, median, and mode from a frequency table?

Multiply each value by its frequency to find the total. For a table of goals scored, 1 goal (2 games), 2 goals (5 games), 3 goals (3 games), the sum is 1×2 + 2×5 + 3×3 = 21 over 10 games, so the mean is 2.1. The mode is 2, the value with the highest frequency. With 10 values, the 5th and 6th are both 2, so the median is 2.

How do you interpret charts to find mean, median, mode, and range?

First, figure out what the chart counts: read the title, axis labels, and scale. Then turn the chart into numbers, either as a list or as value-frequency pairs, and find the total count. On a line plot where each X is one data point, count the X’s above each number. From there, compute each measure as usual. GED questions often add a step, such as how the mean changes when a value is added.

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