Statistics — Mathematics Class 9 Notes (CBSE & HBSE)
Free NCERT Mathematics notes for Statistics (Class 9) on Siksha Sarovar, aligned to CBSE and Haryana Board (HBSE). This chapter is broken into 3 topics with clear explanations, formulas, solved examples and board-pattern practice — free to read, no sign-up required.
Board exam focus — Statistics (CBSE & HBSE)
Closing chapter — data handling. CBSE asks bar graphs, histograms, mean/median/mode. HBSE keeps it lighter, focusing on direct mean and mode for ungrouped data. 5–7 marks.
Data Collection & Presentation
Primary vs Secondary Data
| Type | Source |
|---|---|
| Primary | collected first-hand by the investigator |
| Secondary | drawn from existing sources (books, websites) |
Frequency Distribution
A tabular summary of how often each observation occurs.
- Ungrouped: raw values listed.
- Grouped: observations clustered into class-intervals (e.g. 0–10, 10–20).
Class-Interval Terminology
| Term | Meaning |
|---|---|
| Class width / size | upper − lower limit |
| Class mark | (upper + lower) / 2 |
| Continuous vs Discrete | continuous intervals are 0–10, 10–20…; discrete are 0–9, 10–19… |
| True limits | for discrete data, subtract / add 0.5 to make continuous |
Building a Frequency Table
- Identify range = max − min.
- Decide class width (rule of thumb: 5–10 classes).
- Tally each observation into its class.
- Convert tallies to frequency counts.
CBSE Tip: Always state whether your distribution is inclusive (5–10, 11–15) or exclusive (5–10, 10–15) — the boundary handling differs.
Graphical Representation
Common Graph Types
| Graph | Best For |
|---|---|
| Bar graph | discrete categories |
| Histogram | continuous grouped data (bars touch) |
| Frequency polygon | continuous data — joins midpoints of histogram tops |
Drawing a Bar Graph
- Choose a uniform width and equal gaps for bars.
- y-axis = frequency; x-axis = category labels.
- Bars must start at the same baseline.
Drawing a Histogram
- x-axis: class intervals (no gap between bars).
- y-axis: frequency.
- Bar width = class width.
- Bar height = frequency.
For unequal class widths, height of each bar = frequency × (smallest class width / actual class width).
Drawing a Frequency Polygon
Mark the midpoint of the top of each histogram bar; join consecutive midpoints with straight lines. Extend at both ends to the x-axis by adding two zero-frequency classes.
HBSE Tip: Label axes, units, and bar values; partial marks hinge on labels.
Mean, Median, Mode (Ungrouped Data)
Mean (Arithmetic Average)
For n observations x₁, x₂, …, xₙ: Mean = (x₁ + x₂ + … + xₙ) / n.
For a frequency distribution: Mean = Σ(fᵢ · xᵢ) / Σfᵢ.
Median (Middle Value when Data is Ordered)
- Arrange data in ascending order.
- If n is odd → median = (n + 1)/2-th term.
- If n is even → median = average of (n/2)-th and (n/2 + 1)-th terms.
Mode
The observation that occurs most frequently. There may be no mode (all equal), one mode (unimodal), or more (bimodal, multimodal).
Quick Summary Table
| Measure | Best For |
|---|---|
| Mean | symmetric distributions |
| Median | skewed data with outliers |
| Mode | categorical data |
Empirical Relationship (for moderately skewed data)
Mode ≈ 3 × Median − 2 × Mean.
CBSE Tip: When computing the median, students often forget to sort the data first — always sort before applying the formula.
Frequently asked questions
Are these Statistics notes free?
Yes — the Statistics notes for Mathematics (Class 9) on Siksha Sarovar are completely free to read, with no account required.
Do these notes follow CBSE and HBSE?
Yes. The Statistics notes are NCERT-aligned and include guidance for both CBSE and Haryana Board (HBSE), with important questions and MCQs for revision.
What does the Statistics chapter cover?
Concept explanations, key formulas and definitions, fully solved examples and board-pattern practice questions for Statistics.