Statistics Class 10 Worksheet with Solutions and MCQs
Practise mean, median and mode with this Statistics Class 10 worksheet with solutions. Revise the formula sheet, compare the three methods of finding mean and strengthen your understanding with worked examples, practice questions and MCQs.
Marks scored by students, daily household expenses and the heights of plants are all examples of data. Statistics Class 10 helps you organise such information and describe it using measures of central tendency. Mean gives a weighted average, median identifies a central position, and mode describes the most frequent value or the region of greatest frequency.
In Statistics Class 10 CBSE, grouped frequency distributions are especially important. Instead of individual observations, you work with class intervals and their frequencies. This worksheet page explains how to read these tables, select the correct formula and show calculations clearly. Use it alongside your textbook and the worksheet solutions for regular revision.
Statistics Class 10 Introduction and Key Terms
- Frequency: The number of observations in a class.
- Class interval: A range used to group observations, such as 10–20 or 20–30.
- Class mark: The midpoint of a class, calculated as (lower limit + upper limit) ÷ 2.
- Cumulative frequency: The running total of frequencies.
- Median class: The class containing the central position used in the grouped-data median calculation.
- Modal class: The class with the highest frequency in the usual equal-width grouped distribution.
For grouped continuous data, the exact individual observations are unknown. Calculations using class marks and the grouped median or mode formulas therefore estimate the corresponding measures of the original data.
Statistics Class 10 Formula Sheet
Use this Statistics Class 10 formulas mean median mode chart to revise the main methods. The symbol Σ means “sum of”, and N = Σfi is the total frequency.
| Measure or Method | Formula | Meaning of Symbols |
|---|---|---|
| Mean: direct method | x̄ = Σfixi ÷ N | xi is the class mark; fi is its frequency. |
| Mean: assumed mean method | x̄ = a + (Σfidi ÷ N) | a is the assumed mean; di = xi − a. |
| Mean: step-deviation method | x̄ = a + h(Σfiui ÷ N) | ui = (xi − a) ÷ h; h is a common scaling factor. |
| Median of grouped data | Median = l + [(N/2 − cf) ÷ f] × h | l is the lower boundary of the median class; cf is the cumulative frequency before it; f is its frequency; h is its width. |
| Mode of grouped data | Mode = l + [(f1 − f0) ÷ (2f1 − f0 − f2)] × h | l and h refer to the modal class. f1 is its frequency; f0 and f2 are the preceding and following frequencies. |
What Is “a” in Statistics Class 10?
In the assumed mean and step-deviation methods, a is the assumed mean. Choose a convenient value, usually a class mark near the middle of the table. It simplifies the arithmetic. Choosing another value of a does not change the final mean when the calculations are correct.
Statistics Class 10 Questions with Solutions
The following original practice distribution will be used to calculate mean, median and mode. Intervals follow the continuous convention: 0–10 includes values from 0 up to, but not including, 10.
| Class Interval | Frequency fi | Class Mark xi | fixi | Cumulative Frequency |
|---|---|---|---|---|
| 0–10 | 5 | 5 | 25 | 5 |
| 10–20 | 9 | 15 | 135 | 14 |
| 20–30 | 12 | 25 | 300 | 26 |
| 30–40 | 8 | 35 | 280 | 34 |
| 40–50 | 6 | 45 | 270 | 40 |
| Total | 40 | — | 1010 | — |
Example 1: Mean by the Direct Method
Solution:
N = Σfi = 40
Σfixi = 1010
Mean = 1010 ÷ 40
Mean = 25.25
Multiply each class mark by its frequency. Simply averaging the five class marks would ignore the different numbers of observations.
Mean by Assumed Mean and Step-Deviation Methods
For the same data, choose a = 25. Since the class marks differ by 10, take h = 10 to make the step deviations small integers.
| xi | fi | di = xi − 25 | fidi | ui = di/10 | fiui |
|---|---|---|---|---|---|
| 5 | 5 | −20 | −100 | −2 | −10 |
| 15 | 9 | −10 | −90 | −1 | −9 |
| 25 | 12 | 0 | 0 | 0 | 0 |
| 35 | 8 | 10 | 80 | 1 | 8 |
| 45 | 6 | 20 | 120 | 2 | 12 |
| Total | 40 | — | 10 | — | 1 |
Example 2: Mean by the Assumed Mean Method
Mean = a + (Σfidi ÷ N)
Mean = 25 + (10 ÷ 40)
Mean = 25 + 0.25
Mean = 25.25
Example 3: Mean by the Step-Deviation Method
Mean = a + h(Σfiui ÷ N)
Mean = 25 + 10 × (1 ÷ 40)
Mean = 25 + 0.25
Mean = 25.25
All three methods produce the same mean. Step deviation is particularly convenient when a common factor reduces the deviations to small numbers.
Example 4: Median of the Grouped Data
N/2 = 40 ÷ 2 = 20
The cumulative frequency first exceeds 20 in the class 20–30.
Median class = 20–30
l = 20, cf = 14, f = 12, h = 10
Median = 20 + [(20 − 14) ÷ 12] × 10
Median = 20 + 5
Median = 25
Example 5: Mode of the Grouped Data
The highest frequency is 12, so the modal class is 20–30.
l = 20, f1 = 12, f0 = 9, f2 = 8, h = 10
Mode = 20 + [(12 − 9) ÷ (24 − 9 − 8)] × 10
Mode = 20 + 30/7
Mode ≈ 24.29
Statistics Class 10 MCQ with Answers
-
What is the class mark of 20–30?
A. 10 B. 20 C. 25 D. 30
Answer: C. (20 + 30) ÷ 2 = 25. -
In the assumed mean method, di equals:
A. fi − a B. xi − a C. a − fi D. xi + a
Answer: B. Deviations are calculated from the class marks. -
Which table column helps identify the median class?
A. Class marks B. Cumulative frequency C. Deviations D. Squared class marks
Answer: B. Compare cumulative frequencies with N/2. -
Which class is modal in a standard equal-width distribution?
A. The first class B. The class with the smallest frequency C. The class with the highest frequency D. The last class
Answer: C. Select the class with the greatest frequency.
Statistics Class 10 Practice Questions
-
Find the class marks of 10–20, 20–30 and 30–40.
Answer: 15, 25 and 35. -
Class marks are 5, 15 and 25, with frequencies 2, 4 and 4.
Find the mean.
Answer: (10 + 60 + 100) ÷ 10 = 17. -
An assumed mean is 30, total frequency is 20 and Σfd = −40.
Find the mean.
Answer: 30 − 40/20 = 28. -
Find cumulative frequencies for frequencies 4, 7, 9 and 5.
Answer: 4, 11, 20 and 25. -
A median class has l = 20, h = 10, f = 12 and cf = 14.
If N = 40, find the median.
Answer: 25.
NCERT Exercises and Exam Revision
Use this page alongside your Statistics Class 10 NCERT exercises. Searches for Statistics Class 10 Ex 13.1 often concern mean calculations, while Ex 13.2 and Ex 13.3 commonly refer to mode and median in that numbering. Older editions may use Exercise 14.1, 14.2 and 14.3. Match the actual question with your textbook.
If you are practising Exercise 13.1 solutions by the assumed mean method or step-deviation method, write the additional table columns clearly. For Exercise 13.2 and Exercise 13.3, identify the modal or median class before substituting values. This makes your reasoning easier to follow and helps prevent errors.
After completing routine questions, practise missing-frequency problems, contextual data tables and verified Statistics Class 10 previous year questions. Use a sample paper or worksheet PDF as a timed test, then compare your working with the solutions. Review the method behind each answer rather than memorising the final number.
Related Notes and Worksheets
- Statistics Class 10 Notes and Mind Map for formula revision and a chapter overview.
- Probability Class 10 Notes and Mind Map to study the related topic of chance.
- Arithmetic Progression Class 10 Worksheet with Solutions for additional numerical and algebraic practice.
Frequently Asked Questions
What is “a” in Statistics Class 10?
The symbol a represents the assumed mean. It is a convenient value chosen to simplify deviations in mean calculations. For class marks 5, 15, 25, 35 and 45, choosing a = 25 gives small, manageable deviations.
Do all three methods of finding mean give the same answer?
Yes. Direct, assumed mean and step-deviation methods are algebraically equivalent for the same class marks and frequencies. Differences in final answers usually indicate an arithmetic error or premature rounding.
How do I choose the assumed mean?
Choose a convenient value, usually a class mark near the centre of the distribution. It need not be the actual mean or the class mark of the highest-frequency class. Its purpose is to make calculations easier.
When is the step-deviation method useful?
It is useful when deviations share a convenient common factor. Equal-width classes often make this easy: dividing deviations by the common width produces small integers. Remember to multiply by h when applying the final formula.
How do I identify the median class?
Calculate N/2 and form cumulative frequencies. Locate the class in which the running total passes N/2. If N/2 equals a cumulative frequency exactly, the median lies at the boundary between the adjoining classes.
What does cf mean in the median formula?
cf is the cumulative frequency of the class immediately before the median class. It is not the cumulative frequency of the median class itself. For cumulative frequencies 5, 14, 26, 34 and 40, a median class in the third row uses cf = 14.
How is the modal class different from the median class?
The modal class is selected by the highest frequency in the usual equal-width table. The median class is selected using cumulative frequency and N/2. They may be the same class, but this is not guaranteed.
Should inclusive class intervals be converted before finding median or mode?
Yes, when applying continuous grouped-data formulas, use appropriate class boundaries. For integer-valued intervals 10–19 and 20–29, the corresponding continuous boundaries are 9.5–19.5 and 19.5–29.5. Use the lower boundary in the formula.
Is mode = 3 median − 2 mean always true?
No. It is an empirical approximation often used for moderately skewed distributions, not an exact identity for every dataset. Apply it when the question explicitly asks you to use that relationship or gives an appropriate assumption.
How do I approach missing-frequency questions?
Represent the unknown frequency by a variable. Express the total frequency and any required weighted sum or cumulative frequency in terms of that variable. Substitute the given mean, median or mode into its formula and solve. Check that the result is non-negative and consistent with the selected class.
What is the Statistics Class 10 weightage?
Avoid assuming a fixed chapter-wise mark allocation for every paper. Check the applicable board syllabus, sample paper and marking scheme. Prepare mean, median, mode and interpretation questions across different question formats.
Where can I revise Statistics Class 10 formulas and a mind map?
Visit the Statistics Class 10 notes and mind map page. Then return to this worksheet, attempt the questions independently and check both your table entries and final calculations.
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