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Grouped data questions in Class 10 are long but predictable. You get a frequency table and are asked for the mean, the median, the mode, or all three. The arithmetic is simple; the marks go on choosing the right number from the table. This post works one data set through every method in the syllabus, shows how to check your answers and lists the usual slips.
What does the syllabus ask for in statistics?
The CBSE Mathematics curriculum for Class X (2026-27) lists "mean, median and mode of grouped data (bimodal situation to be avoided)". It expects the mean by the direct, assumed mean and step-deviation methods, and the median and mode "by algebraic method", meaning the formulas. Statistics and probability together carry 11 of the 80 theory marks. The NCERT Class 10 statistics chapter, 2026-27 reprint, derives each formula. Check the curriculum for your exam year.
Here is the data we will use. Marks of 50 students in a test out of 60:
0–10: 5 students
10–20: 8 students
20–30: 11 students
30–40: 16 students
40–50: 6 students
50–60: 4 students
How do you find the mean of grouped data?
Each class is represented by its class mark, the midpoint: (lower limit + upper limit) / 2. The class marks here are 5, 15, 25, 35, 45 and 55.
Direct method. Multiply each frequency by its class mark and add: 5 × 5 + 8 × 15 + 11 × 25 + 16 × 35 + 6 × 45 + 4 × 55 = 25 + 120 + 275 + 560 + 270 + 220 = 1470. Mean = 1470 / 50 = 29.4.
Assumed mean method. Pick a class mark near the middle as the assumed mean, a = 35. Find d = x − 35 for each class: −30, −20, −10, 0, 10, 20. Multiply by frequencies: −150, −160, −110, 0, 60, 80. The sum is −280. Mean = a + (sum of fd) / (sum of f) = 35 + (−280/50) = 35 − 5.6 = 29.4.
Step-deviation method. Divide each d by the class size h = 10 to get u: −3, −2, −1, 0, 1, 2. Then fu: −15, −16, −11, 0, 6, 8, which add to −28. Mean = a + h × (sum of fu) / (sum of f) = 35 + 10 × (−28/50) = 35 − 5.6 = 29.4.
All three give 29.4, as they must. NCERT calls the second and third methods simplified forms of the first. If you have time, doing the mean two ways is a free check.
How do you find the median of grouped data?
Add a cumulative frequency column, a running total: 5, 13, 24, 40, 46, 50.
Find n/2 = 50/2 = 25. The median class is the first class whose cumulative frequency is greater than 25. That is 30–40, with cumulative frequency 40.
Median = l + ((n/2 − cf) / f) × h, where l = 30 is the lower limit of the median class, cf = 24 is the cumulative frequency of the class before it, f = 16 is the frequency of the median class and h = 10.
Median = 30 + ((25 − 24) / 16) × 10 = 30 + 0.625 = 30.625.
How do you find the mode of grouped data?
The modal class is the class with the highest frequency: 30–40, with 16 students.
Mode = l + ((f1 − f0) / (2f1 − f0 − f2)) × h, where f1 = 16 is the modal class frequency, f0 = 11 is the frequency of the class before it and f2 = 6 is the frequency of the class after it.
Mode = 30 + ((16 − 11) / (32 − 11 − 6)) × 10 = 30 + (5/15) × 10 = 30 + 3.33 = 33.33.
The CBSE sample question paper for 2026-27 uses this relation directly, giving the mean and median and asking for the mode, and also has a case-based question asking for the median class and the mode of a table.
What mistakes lose marks in grouped data?
Using a class limit instead of the class mark in the mean. Use the midpoint.
Using the median class's own cumulative frequency for cf. It must be the class before it: 24 here, not 40.
Choosing the median class by frequency, not cumulative frequency.
Swapping f0 and f2. f0 is the class before the modal class, f2 the class after.
Forgetting h in the median or mode formula, which shrinks the correction term to a tenth of its size here.
Classes that are not continuous. If classes are written 10–19, 20–29, NCERT's hint is to convert them to continuous classes such as 9.5–19.5, 19.5–29.5 before using the median formula.
For variance and standard deviation, which come in Class 11, see our post on mean, variance and standard deviation problems. For slips across the whole paper, read our Class 10 maths mistakes list.
A practice routine for statistics
Day 1: Write the median and mode formulas from memory and say in words what each letter means.
Day 2: Take one NCERT table and find the mean by all three methods. They should agree.
Day 3: Find the median and mode of the same table, then test them with the empirical relation.
Day 4: Do two case-based questions under time, writing the cumulative frequency column first every time.
Weekly: One full table, all three measures, in under 12 minutes.
If you are not sure why the median formula works, the Fermi Concept Library has every concept in mathematics with its own lesson, so you can see where the formula comes from before you practise it.
Take any frequency table from your NCERT book today and find its mean two different ways.
