How to Find Mean, Median, Mode, and Range of the Given Data
Read,7 minutes
Mean, median, mode, and range summarize a data set from different angles. On the ACT, the safest habit is to order the data first, then compute only what the question asks.
Core Formulas
- Mean: add all values and divide by the number of values, \(\text{mean}=\frac{\text{sum}}{\text{number of values}}\).
- Median: order the values. The middle value is the median; with an even number of values, average the two middle values.
- Mode: the value or values that occur most often. If every value occurs once, there is no mode.
- Range: subtract the smallest value from the largest value.
Worked Example
For \(8, 12, 12, 15, 18\), the sum is \(65\), so the mean is \(65\div 5=13\). The ordered list shows a median of \(12\), a mode of \(12\), and a range of \(18-8=10\).
Video Lesson
Mean, Median, Mode, and Range of the Given Data
Think of this lesson as more than a rule to memorize. Mean, Median, Mode, and Range of the Given Data is about organizing data and choosing the right summary measure. A strong student does not rush to the first formula on the page; they pause, identify the structure of the problem, and then choose the tool that matches that structure. That pause is what prevents most mistakes.
Statistics is about describing data clearly. First organize the values, then choose the measure or graph that best answers the question being asked.
Here is the teacher way to approach the topic. First, read the problem slowly and underline the information that is actually given. Next, name the target: are you finding a value, simplifying an expression, comparing two quantities, solving for a variable, or interpreting a graph? Once the target is clear, the calculation becomes much less mysterious because every step has a job.
- Read what is given and what is being asked.
- Choose the rule that connects them.
- Substitute carefully and simplify in small steps.
- Check the final answer against the original question.
A helpful habit is to say what each number represents before using it. For example, if a number is a denominator, a radius, a slope, a common difference, or a coefficient, it should not be treated like an ordinary loose number. Its role tells you where it belongs in the formula. This is especially important on ACT-style questions because many wrong answer choices come from using the right numbers in the wrong places.
Another good habit is to keep the work organized vertically. Write one clean line for substitution, one line for simplifying, and one line for the final answer. If the problem has units, keep the units attached. If the problem has signs, exponents, or parentheses, copy them carefully from one line to the next. Most errors in this topic are not caused by a hard idea; they are caused by dropping a negative sign, combining unlike terms, using the wrong denominator, or skipping a check.
When you finish, ask a quick reasonableness question. Should the answer be positive or negative? Should it be larger or smaller than the original number? Does it fit the graph, table, shape, or equation? Can you plug it back into the original problem? This final check turns the lesson from a procedure into understanding.
On a test, the goal is not to write the longest solution. The goal is to write enough clear work that you can see the structure, avoid traps, and recover quickly if one line goes wrong. Practice the examples below with that mindset: identify the type of problem, choose the matching rule, show the substitution, simplify carefully, and check the answer before moving on.
Exercises
Solve each ACT-style practice problem. The questions increase in difficulty.
1) For the data set \( 6, 8, 10, 12, 14 \), find the mean, median, mode, and range.
2) For the data set \( 7, 9, 9, 10, 12 \), find the mean, median, mode, and range.
3) For the data set \( 14, 18, 20, 22, 26, 30 \), find the mean, median, mode, and range.
4) For the data set \( 3, 5, 7, 7, 9, 11 \), find the mean, median, mode, and range.
5) For the data set \( 16, 18, 18, 21, 25, 28, 35 \), find the mean, median, mode, and range.
6) For the data set \( 42, 38, 44, 40, 36, 45 \), find the mean, median, mode, and range.
7) For the data set \( 5, 8, 12, 12, 15, 19, 23, 26 \), find the mean, median, mode, and range.
8) For the data set \( 72, 68, 75, 80, 68, 77, 90 \), find the mean, median, mode, and range.
9) For the data set \( 11, 13, 17, 17, 19, 21, 21, 21 \), find the mean, median, mode, and range.
10) For the data set \( 4, 4, 6, 8, 10, 12, 14, 16, 18 \), find the mean, median, mode, and range.
11) For the data set \( 2, 4, 4, 6, 6, 6, 8, 10 \), find the mean, median, mode, and range.
12) For the data set \( 12.5, 13, 14.5, 15, 16, 16 \), find the mean, median, mode, and range.
13) For the data set \( 58, 61, 63, 64, 65, 66, 98 \), find the mean, median, mode, and range.
14) For the data set \( 81, 84, 84, 86, 90, 91, 95, 97 \), find the mean, median, mode, and range.
15) For the data set \( 100, 92, 88, 88, 75, 92, 96, 99, 88 \), find the mean, median, mode, and range.
16) For the data set \( 23, 27, 31, 35, 39, 43, 47, 51, 55, 59 \), find the mean, median, mode, and range.
17) For the data set \( 6, 6, 9, 12, 15, 18, 18, 18, 21, 24 \), find the mean, median, mode, and range.
18) For the data set \( 48, 52, 52, 56, 60, 64, 68, 68, 72, 76, 80 \), find the mean, median, mode, and range.
19) For the data set \( 4, 9, 9, 14, 19, 24, 29, 34, 39, 44, 49 \), find the mean, median, mode, and range.
20) For the data set \( 120, 135, 140, 145, 150, 150, 155, 160, 175, 180, 185, 190 \), find the mean, median, mode, and range.
Add the values: \(50\). Divide by \(5\): mean \(= 10\).
The median is the middle of the ordered list: \(10\).
The mode is no mode.
The range is \(14-6=8\).
Add the values: \(47\). Divide by \(5\): mean \(= 47/5 \approx 9.40\).
The median is the middle of the ordered list: \(9\).
The mode is 9.
The range is \(12-7=5\).
Add the values: \(130\). Divide by \(6\): mean \(= 65/3 \approx 21.67\).
The median is the middle of the ordered list: \(21\).
The mode is no mode.
The range is \(30-14=16\).
Add the values: \(42\). Divide by \(6\): mean \(= 7\).
The median is the middle of the ordered list: \(7\).
The mode is 7.
The range is \(11-3=8\).
Add the values: \(161\). Divide by \(7\): mean \(= 23\).
The median is the middle of the ordered list: \(21\).
The mode is 18.
The range is \(35-16=19\).
Add the values: \(245\). Divide by \(6\): mean \(= 245/6 \approx 40.83\).
The median is the middle of the ordered list: \(41\).
The mode is no mode.
The range is \(45-36=9\).
Add the values: \(120\). Divide by \(8\): mean \(= 15\).
The median is the middle of the ordered list: \(\frac{27}{2}\).
The mode is 12.
The range is \(26-5=21\).
Add the values: \(530\). Divide by \(7\): mean \(= 530/7 \approx 75.71\).
The median is the middle of the ordered list: \(75\).
The mode is 68.
The range is \(90-68=22\).
Add the values: \(140\). Divide by \(8\): mean \(= 35/2 \approx 17.50\).
The median is the middle of the ordered list: \(18\).
The mode is 21.
The range is \(21-11=10\).
Add the values: \(92\). Divide by \(9\): mean \(= 92/9 \approx 10.22\).
The median is the middle of the ordered list: \(10\).
The mode is 4.
The range is \(18-4=14\).
Add the values: \(46\). Divide by \(8\): mean \(= 23/4 \approx 5.75\).
The median is the middle of the ordered list: \(6\).
The mode is 6.
The range is \(10-2=8\).
Add the values: \(87\). Divide by \(6\): mean \(= 29/2 \approx 14.50\).
The median is the middle of the ordered list: \(\frac{59}{4}\).
The mode is 16.
The range is \(16-12.5=3.5\).
Add the values: \(475\). Divide by \(7\): mean \(= 475/7 \approx 67.86\).
The median is the middle of the ordered list: \(64\).
The mode is no mode.
The range is \(98-58=40\).
Add the values: \(708\). Divide by \(8\): mean \(= 177/2 \approx 88.50\).
The median is the middle of the ordered list: \(88\).
The mode is 84.
The range is \(97-81=16\).
Add the values: \(818\). Divide by \(9\): mean \(= 818/9 \approx 90.89\).
The median is the middle of the ordered list: \(92\).
The mode is 88.
The range is \(100-75=25\).
Add the values: \(410\). Divide by \(10\): mean \(= 41\).
The median is the middle of the ordered list: \(41\).
The mode is no mode.
The range is \(59-23=36\).
Add the values: \(147\). Divide by \(10\): mean \(= 147/10 \approx 14.70\).
The median is the middle of the ordered list: \(\frac{33}{2}\).
The mode is 18.
The range is \(24-6=18\).
Add the values: \(696\). Divide by \(11\): mean \(= 696/11 \approx 63.27\).
The median is the middle of the ordered list: \(64\).
The mode is 52, 68.
The range is \(80-48=32\).
Add the values: \(274\). Divide by \(11\): mean \(= 274/11 \approx 24.91\).
The median is the middle of the ordered list: \(24\).
The mode is 9.
The range is \(49-4=45\).
Add the values: \(1885\). Divide by \(12\): mean \(= 1885/12 \approx 157.08\).
The median is the middle of the ordered list: \(\frac{305}{2}\).
The mode is 150.
The range is \(190-120=70\).
