Grouped Data: Make a Table Fast (With Examples)

Key takeaways
Grouped data turns a long list into ranges so you can see patterns faster.
Pick a class width (size of each range), then tally counts into a grouped frequency table.
Grouping is great for big data sets, but it gives approximate results.

Grouped data is what you use when your list is too long to read. You will learn a simple method and see worked examples. You’re not behind. You just need a clear method.

Quick answer

Grouped data means you replace many exact values with class intervals (number ranges) and their counts.
To make it: Step 1 pick a class width, Step 2 write class intervals, Step 3 tally, Step 4 total your frequencies.
This is the same idea used to build histograms (bar graphs with bins).

What is grouped data?

Grouped data (data shown in ranges instead of exact values).
You keep the big picture (how values are spread out), but you lose some detail.

Key terms

Frequency (how many times something happens).
Class interval (a range like 60–69).
Class width (the size of the range; for 60–69, width is 10).
Midpoint / class mark (middle of the interval; used for grouped mean).
Histogram (a graph that uses bins/intervals to show a distribution).

When should you use grouped data?

Use grouped data when:

You have many values (like 30+ scores).
The data covers a wide range (like 3 to 98).
You need a histogram or a quick summary.

Don’t group when:

You only have a few values (like 8 numbers).
You need exact values (like “Who got 100?”).

Grouped vs ungrouped: what changes?

You have…	Sample Data	Best choice	Why
Short list	8, 10, 12, 15, 17	Ungrouped table	Keeps exact values. Easy to read without ranges.
Long list	42, 45, 48, 51, 55, 58, 62, 64, 73, 77, 81, 83, 88, 90, 92	Grouped frequency table	Faster to see patterns when data is many.
Need a graph	Test scores from 0–100 for 40 students	Grouped (bins)	Histograms use intervals (like 40–49, 50–59).

Step-by-step: How to make a grouped frequency table

Step 1: Find your range

Range (max − min).
Example: min = 42, max = 88 → range = 46.

Step 2: Choose a class width

A common classroom choice is a simple width like 2, 5, or 10, and around 5–15 classes so the table is readable. (This is a rule of thumb, not a law.)

Quick width hack:

If numbers look like test scores (0–100), start with width 10.
If numbers are small (0–30), start with width 5.

When the class width needs to be computed, the most commonly accepted classroom formula is:

Class Width Formula

$\textbf{Class Width} \approx \frac{\text{Maximum value} – \text{Minimum value}}{\text{Number of classes}}$

In words:

Class width = Range ÷ Number of classes

Range = Highest value − Lowest value
Number of classes = how many rows (usually 5–15 for school work)

How to choose the number of classes

There is no single “perfect” number, but these are widely accepted:

Rule of Thumb

Use 5 to 10 classes
Pick a number that makes clean intervals (5, 10, 20)

Square-Root Rule (Very Common in Textbooks)

$k \approx \sqrt{n}$

$k$ = number of classes
$n$ = number of data values

Example:
If $n = 36$ , then $k ≈ \sqrt{36} = 6$ classes.

Step 3: Write class intervals (no overlap)

Example with width 10:

Start at least lower limit (here, least lower limit is 40) or a rounded value near your minimum data.

First bin: 40–49
Add width (10):
- Lower limit: 40 + 10 = 50
- Upper limit: 49 + 10 = 59
  → Second bin: 50–59
Repeat:
- 50–59 → 60–69
- 60–69 → 70–79
- 70–79 → 80–89

Final intervals:
40–49, 50–59, 60–69, 70–79, 80–89

Keep them:

Same width (each interval size matches)
No overlap (a value fits only one class)

Step 4: Tally and count frequencies

Go through the list once. Add a tally mark to the right class.

Step 5: Total check (quick self-check)

Add all frequencies. The total must equal n (how many data values you started with).

What to write on your paper (mini-checklist)

Min, max, range
Chosen/computed class width = ___
Class intervals (written neatly)
Tally marks
Frequency totals + total n check

Template table (copy this)

Class interval	Tally	Frequency
–
–
–
Total		n =

Worked examples

Example 1 (very easy): Make grouped data

Data (n=10): 42, 45, 48, 51, 55, 58, 62, 64, 73, 77

Step 1: min=42, max=77 → range=35
Step 2: choose width = 10
Step 3: intervals: 40–49, 50–59, 60–69, 70–79
Step 4: tally and count

Class interval	Frequency
40–49	3
50–59	3
60–69	2
70–79	2
Total	10

Why this works: every number fits exactly one interval.

Example 2 (typical homework): Build a grouped frequency table

Quiz scores (n=20):
53, 55, 56, 57, 59, 60, 61, 63, 64, 65, 66, 68, 70, 72, 73, 74, 78, 81, 83, 89

Pick width = 10. Start at 50.

Intervals: 50–59, 60–69, 70–79, 80–89

Class interval	Frequency
50–59	5
60–69	7
70–79	6
80–89	2
Total	20

Quick self-check (total frequency): 5+7+6+2 = 20 ✅

Example 3 (a common “trap”): Boundary value

Data includes a 60. Your classes are 50–59 and 60–69.

Where does 60 go?
It goes in 60–69, not 50–59.
That’s why your intervals must be clear and not overlapping.

Example 4 (short): Class width is computed

Data (n=15): 42, 45, 48, 51, 55, 58, 60, 62, 64, 68, 70, 73, 77, 81, 88

Min = 42, Max = 88 → Range = 46
Choose classes using $k \approx \sqrt{n}=\sqrt{15}\approx3.9\rightarrow 4$
Class width: $46 \div 4 = 11.5 \rightarrow$ round up to 12

Use a clean start at 40:

Class interval	Frequency
40–51	4
52–63	4
64–75	4
76–87	2
88–99	1

Check (total frequency): 4+4+4+2+1 = 15 ✅

What grouped data is used for: mean and median (approx.)

Mean of grouped data (estimate)

When data is grouped, the mean is usually found using midpoints: $\text{Grouped mean} \approx \frac{\sum (f \cdot m)}{\sum f}$ Grouped mean≈∑f

$f$ = frequency (count)
$m$ = class midpoint (middle of the interval)

Why “≈”? You don’t know the exact values inside each bin. You only know the range.

Median of grouped data (estimate)

A common method uses the median class and cumulative frequency.
If your teacher requires it, use your class notes or a trusted guide, because class boundary rules can vary.

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Practice set (with answer key)

Directions: Make a grouped frequency table. Use the given class width.

Data: 11, 12, 15, 18, 19, 21, 22, 24, 25, 27 (width 5)
Data: 42, 44, 45, 49, 50, 51, 55, 57, 60, 61, 63, 66 (width 10)
Data: 3, 4, 4, 6, 7, 9, 10, 10, 12, 13, 14 (width 5)
Data: 90, 91, 92, 95, 97, 99, 100, 100, 100 (width 5)
Trap: Data: 20, 25, 30, 35, 40 (width 10). Use classes 20–29, 30–39, 40–49. Where does 30 go?

Answer key (frequencies only)

Classes 10–14: 2; 15–19: 3; 20–24: 3; 25–29: 2
40–49: 4; 50–59: 4; 60–69: 4
0–4: 3; 5–9: 3; 10–14: 5
90–94: 3; 95–99: 3; 100–104: 3
30 goes in 30–39 (not 20–29)

Short solutions (2 items)

#1: Count values in each bin: 10–14 has (11,12)=2; 15–19 has (15,18,19)=3; 20–24 has (21,22,24)=3; 25–29 has (25,27)=2.
#5: The class 30–39 includes 30 by definition. Classes do not overlap.

Common mistakes

Mistake	Why it happens	Do this instead
Picking random class widths	You want to finish fast	Use a simple width (2, 5, 10) and keep it consistent
Making overlapping intervals (like 50–60 and 60–70)	The endpoints confuse you	Use clear bins like 50–59 and 60–69
Forgetting to total frequencies	You assume it’s fine	Add frequencies. Make sure total = n
Starting intervals at a weird number	You copy min exactly	Round down to a clean start (like 50 instead of 53)
Treating grouped mean as exact	You forget it’s a summary	Write “≈” or “estimate” for grouped mean

If you get stuck…

“I don’t know what class width to use.”
Try 5 or 10. Choose a width that makes about 5–15 rows.
“My totals don’t match n.”
Recount one bin at a time. Check boundary values (like 60, 70).
“I keep mixing up intervals.”
Draw a quick number line with your bins. (This prevents overlap.)
“My teacher wants mean/median from grouped data.”
Review the midpoint method for mean and use your course rule for median class boundaries (it can vary).
“My calculator gives a different answer.”
If you used grouped data, your answer is an estimate, not the exact ungrouped result.

What else would help

Frequency table (learn how to construct a frequency table)
Class interval and class width (learn how to pick clean bins fast)
Mean of grouped data (use midpoints to estimate the average)
Median of grouped data (use cumulative frequency to locate the middle class)

How we know

Grouped frequency tables and histograms are standard introductory statistics tools.
The “bins/intervals” idea matches how major references define histograms and binning.
The grouped-mean midpoint method is a widely taught classroom method.
The “reasonable number of intervals” idea is presented as a rule of thumb (not a guarantee).
Steps were checked against the worked examples and total-frequency checks.

Use this the right way

Use this guide to understand the method and practice it. Then do your own work on your own data. If this is for a research project, report your steps clearly and cite any formulas or notes your teacher requires.

Study tools that can help

If you get distracted easily: a dedicated math notebook so your tables stay neat and easy to check.
- Best high-quality notebooks for math notes
If your tallies get messy: graph paper (or a ruled notebook) to keep columns straight.
If you make boundary mistakes: a simple ruler + number line sketch beside your table.

References

OpenStax. (2023). Introductory Statistics 2e: 1.3 Frequency, frequency tables, and levels of measurement. OpenStax.

OpenStax. (2023). Introductory Statistics 2e: 2.2 Histograms, frequency polygons, and time series graphs. OpenStax.

National Institute of Standards and Technology. (2001). Binned (frequency table). NIST/SEMATECH e-Handbook of Statistical Methods (Dataplot reference). https://www.itl.nist.gov/div898/software/dataplot/refman2/auxillar/binned.htm

LibreTexts. (2025). Measures of median and mean on grouped data. Statistics LibreTexts.

University of Baltimore. (n.d.). Frequency distributions. Math and Statistics Guides (Pressbooks). https://ubalt.pressbooks.pub/mathstatsguides/chapter/frequency-distributions/

Grouped Data: Make a Table Fast (With Examples)

Quick answer