Chapter 13 · Class X Mathematics · NCERT Exercises

Statistics — Exercises

Mean · Median · Mode — All Class X Statistics Exercises Solved

📂 3 Exercises 📝 22 Questions 🎓 Moderate

▶ Start Exercises 📖 Revise Notes

Exercise Index

Mean by direct method, assumed mean (deviation), and step-deviation

Mode of grouped data; modal class; mode formula

6 Q Easy-Moderate

Median of grouped data; cumulative frequency; median formula

3 exercise files · 22 total questions

Chapter at a Glance

CBSE BoardsNTSE

9 Concepts

10 Formulas

Moderate Difficulty

7–9% Weightage

Before You Begin

Prerequisites

✓Mean, median, mode of ungrouped data (Class IX)
✓Frequency tables
✓Basic graph plotting

Have Ready

🔧Graph paper for ogive
🔧Frequency distribution table template
🔧Calculator

Exercise Topic Map

Exercise 13.1 Direct: x̄ = Σfx/Σf; Assumed mean: x̄ = A + Σfd/Σf; Step-deviation: x̄ = A + (Σfu/Σf)×h

Exercise 13.2 Modal class = class with highest frequency; Mode = l + [(f₁−f₀)/(2f₁−f₀−f₂)]×h

Exercise 13.3 cf table; locate n/2; median class; Median = l + [(n/2−cf)/f]×h

Key Formulae — Recall Before Solving

\(\bar{x} = A + \dfrac{\sum f_i d_i}{\sum f_i},\quad d_i = x_i - A \quad \text{(Assumed Mean)}\)

\(\text{Mode} = l + \dfrac{f_1 - f_0}{2f_1 - f_0 - f_2} \times h\)

\(\text{Median} = l + \dfrac{\tfrac{n}{2} - cf}{f} \times h\)

\(3\,\text{Median} = \text{Mode} + 2\,\text{Mean} \quad \text{(Empirical relation)}\)

NCERT Solving Method

Step 1 — Always compute class midpoints xᵢ as (lower+upper)/2 for grouped data. Step 2 — Mean: set up table with columns: class | f | x | fx (or fd or fu); compute column by column. Step 3 — Mode: identify modal class (highest f); substitute l, f₀, f₁, f₂, h carefully. Step 4 — Median: build cumulative frequency column; find n/2; locate the median class; apply formula. Step 5 — Ogive: plot (upper boundary, cf) for less-than; (lower boundary, cf) for more-than; intersection x-coordinate = median.

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