GROUPED DATA • MEAN • MEDIAN • MODE
Statistics Worksheet
with Online Quiz and Activities
Read the table, choose the method and explain what your answer represents. Explore grouped data with clickable classes and calculation labs.
Read the Data
Identify frequencies, class marks and running totals.
Explore the tables →Choose Your Method
Connect direct, assumed-mean and step-deviation calculations.
Try the calculation labs →Explain the Result
Repair errors, find missing values and interpret a survey.
Build exam confidence →Statistics Online Quiz
Question 1 of 20 • Easy • Answered 0/20
Find the class mark of 10–20.
Quiz instructions
Attempt 10 easy, five average and five HOTS questions in 20 minutes. The timer begins with your first answer or navigation. Selecting an option opens the next question. Use Previous or the numbered buttons to revisit answers. One mark per correct answer, with no negative marking. Solutions appear after submission or timeout.
Interactive Statistics Games
Find the Class
Tap a table row or a class button.
Select the modal class.
| Class | Frequency |
|---|---|
| 4 | |
| 7 | |
| 12 | |
| 9 | |
| 3 |
Continuous classes include their lower limit and exclude their upper limit.
Show frequency histogram
Choose your game
Select a class, build cumulative frequencies, move an assumed mean, sort clues or arrange a solution. The raised selector switches between five games, each containing five tasks.
Mean Median and Mode Calculation Activities
Answer entry help
Enter numbers without units. Fractions such as 305/12 are accepted. Give non-terminating decimals to at least three places. Keep intermediate calculations exact. All displayed classes use the lower-inclusive, upper-exclusive convention unless a task explicitly discusses inclusive integer classes.
Extra Statistics Practice
Missing Values Challenge
Form an equation from the information given.
The grouped mean is 1650/30. Find the missing frequency x.
| Class | Frequency |
|---|---|
| 30–40 | 3 |
| 40–50 | x |
| 50–60 | 11 |
| 60–70 | 8 |
| 70–80 | 2 |
Continuous classes include their lower limit and exclude their upper limit.
Enter a number or fraction, such as 305/12. Give non-terminating decimals to at least three places.
Explore the extra sets
Find missing frequencies, correct errors, transform data, analyse reading times and create valid distributions. Each set contains five tasks. Entries stay available while this page remains open.
Statistics Revision Tips for Students
- Add frequencies before substituting N.
- Calculate each class mark from both class limits.
- Keep the sign of a negative deviation.
- In step deviation, multiply the average step deviation by h.
- Build cumulative frequencies in class order and compare them with N/2.
- Use the cumulative frequency before the median class, not within it.
- For mode, distinguish f₀, f₁ and f₂.
- State that results from grouped intervals are estimates, and use the empirical relationship only when instructed.
Teaching Tips for Parents and Teachers
- Ask learners to distinguish a frequency from a class mark.
- Use the assumed-mean slider to show why the choice of a does not change the grouped mean.
- Compare a modal class with the numerical mode estimate.
- Discuss why grouping loses the exact individual observations.
- Ask students to explain which symbol caused an incorrect solution.
Statistics Notes Formulas and Solved Questions
This Statistics Class 10 worksheet focuses on mean, median and mode of grouped data. Start by reading class intervals and frequencies accurately. The online quiz checks concepts, while interactive tables let you build cumulative frequencies and practise each method beside the data. Use the existing worksheet download option for written work.
Statistics Class 10 Mean Median and Mode Explained
The mean is a weighted average. The median describes a middle position. The mode identifies the most frequent value or, for a grouped table, an estimate within the modal class. These measures answer different questions and need not be equal.
Statistics Class 10 Formula Sheet
Let N=Σfᵢ, xᵢ be a class mark, a an assumed mean and h the common class width in step deviation. For median and mode, l is the lower class boundary of the selected class.
| Method | Formula |
|---|---|
| Class mark | xᵢ=(lower limit+upper limit)/2 |
| Direct mean | x̄=Σfᵢxᵢ/N |
| Assumed mean | x̄=a+Σfᵢdᵢ/N, with dᵢ=xᵢ−a |
| Step deviation | x̄=a+h(Σfᵢuᵢ/N), with uᵢ=(xᵢ−a)/h |
| Grouped median | l+[(N/2−cf)/f]h |
| Grouped mode | l+[(f₁−f₀)/(2f₁−f₀−f₂)]h |
| Empirical estimate when instructed | Mode ≈ 3Median−2Mean |
Direct Assumed Mean and Step Deviation Methods
The direct method multiplies each class mark by its frequency. The assumed-mean method uses deviations from a convenient value a to simplify arithmetic. Step deviation divides those deviations by the common class width h. The three methods give the same grouped mean when calculations are consistent. Choosing a central class mark can make the work shorter; it is a convenience rather than a condition for correctness.
How to Find the Median Class and Modal Class
For the median class, form less-than cumulative frequencies and locate the first cumulative frequency greater than N/2. Then use cf from the preceding class. For equal-width classes with a unique peak, the modal class has the largest frequency. Its midpoint is not automatically the mode, and the highest frequency itself is not the mode.
Statistics Class 10 Examples with Solutions
Find grouped mean by the direct method
For classes 0–10, 10–20 and 20–30, the frequencies are 5, 8 and 7.
Class marks are 5, 15 and 25.
N=5+8+7
N=20
Σfᵢxᵢ=5×5+8×15+7×25
Σfᵢxᵢ=320
Mean=320/20
Mean=16
Find a grouped median
For classes 0–10, 10–20, 20–30 and 30–40, frequencies are 4, 8, 12 and 6.
N=30
N/2=15
Cumulative frequencies are 4, 12, 24 and 30.
Median class is 20–30.
Median=20+[(15−12)/12]×10
Median=22.5
Find a grouped mode
Use the same four-class table. The modal class is 20–30, so l=20, h=10, f₁=12, f₀=8 and f₂=6.
Mode=20+[(12−8)/(24−8−6)]×10
Mode=20+(4/10)×10
Mode=24
Statistics Class 10 Missing Frequency Questions
When a frequency is unknown, include it in N as well as in weighted products or cumulative totals. With a given mean, write Σfᵢxᵢ=Mean×Σfᵢ. With a given median, identify the relevant class and express N, cf and f correctly before substitution. Two unknown frequencies usually require two independent conditions, such as total frequency and mean.
Find a missing frequency from mean
Classes 0–10, 10–20 and 20–30 have frequencies 6, x and 10. Their grouped mean is 17.
(6×5+15x+10×25)/(16+x)=17
280+15x=17(16+x)
280+15x=272+17x
8=2x
x=4
Statistics Class 10 Important Questions
Practise class marks, cumulative frequencies, all three mean methods, median and modal class selection, grouped estimates, missing frequencies and error correction. A case-based table can ask for several measures from the same distribution. These are useful revision types rather than predictions of a future board paper.
Statistics Class 10 Case-Based Questions
A daily reading survey
A survey groups reading times into 0–10, 10–20, 20–30 and 30–40 minutes. Frequencies are 3, 7, 8 and 2.
How many students took part?
N=3+7+8+2
N=20
Which is the modal class? It is 20–30 minutes because frequency 8 is the greatest.
What is the grouped mean?
Σfᵢxᵢ=3×5+7×15+8×25+2×35
Σfᵢxᵢ=390
Mean=390/20
Mean=19.5 minutes
Statistics Class 10 Extra Questions with Answers
- Find the class mark of 35–45.
View solution
x=(35+45)/2
x=40
- Frequencies are 6, 9, 5 and 10. Form cumulative frequencies.
View solution
The running totals are 6, 15, 20 and 30.
- If a=30, Σfᵢdᵢ=75 and N=25, find mean.
View solution
Mean=30+75/25
Mean=33
- If a=50, h=10, Σfᵢuᵢ=−8 and N=40, find mean.
View solution
Mean=50+10×(−8/40)
Mean=48
- When instructed to use the empirical relationship, mean=22 and median=24. Estimate mode.
View solution
Mode≈3×24−2×22
Mode≈28
Class Boundaries and Grouped Data Estimates
In the displayed continuous tables, 20–30 includes 20 and excludes 30. For integer classes such as 10–19 and 20–29, convert to continuous boundaries when required; a 0.5 correction produces 9.5–19.5 and 19.5–29.5. Grouping does not preserve every observation, so the underlying raw-data mean, median and mode cannot generally be recovered exactly. The grouped formulas provide representative estimates.
Current Syllabus and Official Sample-Paper Update
The official CBSE Mathematics syllabus for 2026–27 covers grouped-data mean, median and mode, including direct, assumed-mean and step-deviation mean methods, and specifies avoiding bimodal cases. The current official Mathematics Standard sample paper includes a grouped-marks case study and a mean–median–mode relationship question. Practise interpreting a table as well as substituting formulas. These are verified sample-paper themes, not a ranking of questions repeated in actual board exams.
Common Statistics Mistakes to Avoid
Do not divide by the number of classes instead of total frequency, average class marks without weights, omit h in step deviation, use the wrong cf in median, confuse f₀ with f₂, or treat the empirical relationship as an exact identity. Keep enough precision until the final answer.
Related Maths Worksheets and Revision
Statistics Frequently Asked Questions
What is the difference between mean median and mode?
Mean is a weighted average, median describes the middle position and mode describes the most frequent value or modal region. They need not be equal.
Do direct assumed-mean and step-deviation methods give the same answer?
Yes. Used consistently on the same class marks and frequencies, all three give the same grouped mean. Assumed mean and step deviation simplify the arithmetic.
How do I find the class mark of an interval?
Add its lower and upper limits and divide by two. For 30–40, the class mark is 35. Class marks represent intervals in the grouped mean calculation.
How do I identify the median class?
Find N/2 and build cumulative frequencies. Select the first class whose cumulative frequency is greater than N/2. If N/2 falls exactly on a cumulative boundary, interpolation reaches that shared boundary.
Which cumulative frequency goes into the median formula?
Use the cumulative frequency of the class immediately before the median class. In the first class, that preceding cumulative frequency is zero.
Is the modal class the same as the numerical mode?
No. For equal-width classes, the modal class is the interval with the greatest frequency. The grouped mode formula estimates a value within that interval using the neighbouring frequencies.
What do f₀ f₁ and f₂ mean in the mode formula?
f₁ is the modal-class frequency, f₀ is the preceding class frequency and f₂ is the following class frequency. Read them in class order rather than sorting the frequency values.
How do I solve missing-frequency questions?
Include the unknown frequency in all relevant totals. Use the given mean or median to form an equation. With two unknown frequencies, use two independent conditions, such as total frequency and mean, then check positive integer answers.
Is mode equal to three times median minus twice mean?
This is an empirical approximate relationship, not an exact identity for every distribution. Use it when the question instructs you to estimate using that relationship.
Why are grouped-data answers estimates?
The table tells you how many observations fall in each interval, but not their exact individual values. Class marks and interpolation represent those unknown values, so the original raw-data measures cannot generally be recovered exactly.
When should I convert class limits to class boundaries?
If recorded integer classes leave gaps, such as 10–19 and 20–29, make them continuous when required for interpolation. A 0.5 correction gives 9.5–19.5 and 19.5–29.5. Already continuous classes such as 10–20 and 20–30 do not need that correction.
Which Statistics questions should I practise for exams?
Practise all three mean methods, cumulative frequency, median and modal class identification, grouped median and mode, missing frequencies and case-based tables. Check totals, symbols and the final unit before submitting.
Can You Explain the Story Behind the Table?
Choose a method, calculate carefully and interpret your result.
Start the Statistics Online Quiz
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