CBSE Class 10 Mathematics • Chapter 13 • Revision 2026
Statistics Class 10
Revise grouped data with our Statistics Class 10 notes and mind map PDF. The PDF contains notes and a mind map for organising your revision. Use this page to understand mean, median and mode formulas, follow solved examples and clear common doubts before practising questions.
Statistics helps us summarise information such as test scores, daily temperatures and the time students spend reading. Instead of studying every observation separately, we use a representative value. In Class 10 Statistics, you calculate the mean, median and mode of grouped frequency distributions.
The chapter becomes easier when you understand the symbols before substituting numbers. A class mark is different from a class limit, frequency is different from cumulative frequency, and the median class need not be the modal class. These notes explain those differences with one frequency table used throughout the examples.
Statistics Class 10 Notes: Important Terms
- Frequency: The number of observations in a class.
- Class interval: A group such as 10–20 or 20–30.
- Class mark: The midpoint of a class interval.
- Class width: The difference between its upper and lower boundaries.
- Cumulative frequency: A running total of frequencies.
- Mean: A frequency-weighted average calculated using class marks.
- Median: The value dividing the distribution into two equal parts.
- Mode: An estimate of the most frequent value in the distribution.
Finding a Class Mark
Class mark = (lower limit + upper limit) ÷ 2.
For the interval 20–30:
Class mark = (20 + 30) ÷ 2
= 25.
Use class marks, rather than just lower or upper limits, when calculating the mean of grouped data.
Statistics Class 10 Formula Sheet
| Method or Measure | Formula | Meaning of Symbols |
|---|---|---|
| Direct method | Mean = Σfixi ÷ Σfi | fi = frequency; xi = class mark. |
| Assumed mean method | Mean = a + (Σfidi ÷ Σfi) | a = assumed mean; di = xi − a. |
| Step deviation method | Mean = a + h(Σfiui ÷ Σfi) | ui = (xi − a) ÷ h; h is a common scaling factor, usually the equal class width. |
| Median | Median = l + [(N/2 − cf) ÷ f] × h | l = lower boundary of median class; cf = cumulative frequency before it; f = its frequency; h = its width; N = total frequency. |
| Mode | Mode = l + [(f1 − f0) ÷ (2f1 − f0 − f2)] × h | f1 = modal-class frequency; f0 = preceding frequency; f2 = succeeding frequency. |
| Empirical relationship | Mode ≈ 3 Median − 2 Mean | An approximate relationship for suitable distributions, not an identity for every data set. |
Use Continuous Class Boundaries
Before applying grouped median and mode formulas, check that the classes are continuous. For integer-valued data grouped as 10–19, 20–29 and 30–39, the corresponding boundaries are 9.5–19.5, 19.5–29.5 and 29.5–39.5. Use the correct lower boundary in the formula.
Statistics Class 10 Questions with Solutions
Consider this grouped distribution of scores. The intervals are interpreted as 0 ≤ score < 10, 10 ≤ score < 20, and so on.
| Score | Frequency f | Class Mark x | fx | Cumulative Frequency |
|---|---|---|---|---|
| 0–10 | 4 | 5 | 20 | 4 |
| 10–20 | 6 | 15 | 90 | 10 |
| 20–30 | 10 | 25 | 250 | 20 |
| 30–40 | 8 | 35 | 280 | 28 |
| 40–50 | 2 | 45 | 90 | 30 |
| Total | 30 | — | 730 | — |
Example 1: Mean by the Direct Method
Mean = Σfx ÷ Σf
= 730 ÷ 30
= 24.333…
≈ 24.33 marks.
Each class mark is multiplied by its frequency. Adding only the class marks and dividing by the number of classes would ignore how many observations belong to each class.
Example 2: Mean by the Assumed Mean Method
Choose a = 25.
The deviations x − a are −20, −10, 0, 10 and 20.
Σfd = 4(−20) + 6(−10) + 10(0) + 8(10) + 2(20)
= −80 − 60 + 0 + 80 + 40
= −20
Mean = a + Σfd ÷ Σf
= 25 + (−20 ÷ 30)
= 25 − 0.666…
≈ 24.33 marks.
The assumed mean is a convenient starting value. It does not have to equal the final mean.
Example 3: Mean by the Step Deviation Method
Choose a = 25 and h = 10.
The values of u = (x − a) ÷ h are −2, −1, 0, 1 and 2.
Σfu = 4(−2) + 6(−1) + 10(0) + 8(1) + 2(2)
= −8 − 6 + 0 + 8 + 4
= −2
Mean = a + h(Σfu ÷ Σf)
= 25 + 10(−2 ÷ 30)
= 25 − 0.666…
≈ 24.33 marks.
All three methods produce the same result when applied correctly.
Example 4: Median of Grouped Data
N = 30
N/2 = 15
The cumulative frequency first exceeds 15 in the class 20–30. Therefore, this is the median class.
l = 20, cf = 10, f = 10 and h = 10.
Median = l + [(N/2 − cf) ÷ f] × h
= 20 + [(15 − 10) ÷ 10] × 10
= 20 + 5
= 25 marks.
Example 5: Mode of Grouped Data
The highest frequency is 10, so the modal class is 20–30.
l = 20, h = 10, f1 = 10,
f0 = 6 and f2 = 8.
Mode = 20 + [(10 − 6) ÷ (20 − 6 − 8)] × 10
= 20 + (4 ÷ 6) × 10
= 20 + 6.666…
≈ 26.67 marks.
Statistics Class 10 Mind Map and Revision Plan
Organise your Statistics Class 10 mind map into four branches: data and class marks, mean methods, median and mode. Under mean, connect direct, assumed mean and step deviation methods. Under median, connect N/2 to cumulative frequency. Under mode, connect the highest frequency to the modal class.
For your 2026 revision, first recall the formulas without looking. Then complete a frequency table and calculate all three measures. This gives you practice in selecting the correct class, interpreting symbols and checking calculations rather than simply memorising formulas.
A Useful Answer Check
The calculated median should lie within the median class, and the calculated mode should lie within the selected modal class in a standard textbook example. The mean should lie between the smallest and largest class marks. An answer outside these ranges is a reason to check your substitutions and arithmetic.
Practise Statistics Questions
Apply these methods using the Statistics Class 10 worksheet . Attempt the calculations before checking the answers.
Revise chance and outcomes with Probability Class 10 notes and mind map , or explore the CBSE Class 10 Maths notes collection .
Frequently Asked Questions
What is a in Statistics Class 10?
The symbol a represents the assumed mean in the assumed mean and step deviation methods. Choose a convenient value, usually a class mark near the centre of the distribution, to simplify subtraction.
Can I choose any assumed mean?
Yes. A different assumed mean changes the deviations but not the final mean. A central class mark usually keeps the deviations small and makes the calculation easier.
Do the three mean methods give different answers?
No. Direct, assumed mean and step deviation methods are equivalent ways to calculate the same grouped mean. Different answers usually indicate an arithmetic, sign or rounding error.
What is cf in the median formula?
It is the cumulative frequency of the class immediately before the median class. In the example above, the median class is 20–30 and cf is 10. Do not use the cumulative frequency of the median class itself.
How do I identify the median class?
Find N/2 and locate it in the cumulative frequency column. Select the class where the running total first reaches or exceeds N/2. If N/2 exactly matches a cumulative total, the median is at the shared boundary of the adjacent continuous classes.
Are the median class and modal class always the same?
No. The median class is located using N/2 and cumulative frequency. The modal class is identified by the highest frequency. These methods can select different classes.
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 succeeding class frequency. Label them in the table before substituting values.
Is Mode = 3 Median − 2 Mean always exact?
No. It is an empirical approximation for suitable distributions. Use it when a question asks you to apply that relationship. When a frequency table is supplied, use the appropriate grouped formula unless instructed otherwise.
Are grouped mean, median and mode exact original-data values?
Grouping hides individual observations. Calculating with class marks and interpolation therefore gives representative estimates based on the grouped distribution. Keep this distinction in mind when interpreting the answers.
Is Statistics Chapter 13 or Chapter 14?
Statistics is Chapter 13 in the current NCERT Class 10 Maths textbook. Older editions may label it Chapter 14. Match the chapter name and full question when using exercise solutions.
What does the Statistics Class 10 PDF contain?
The PDF contains notes and a mind map. Use them for concept revision and formula recall, then practise questions to strengthen your calculation skills.
Which mistakes should I check before submitting my answer?
Check class marks, frequency totals, negative deviations, continuous boundaries and the cf value. In step deviation, remember to multiply the correction by h. Round at the final stage whenever possible.
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