Knowledge organisers

Statistics: CBSE Class 9 Maths knowledge organiser

Everything to know about statistics on one page: key definitions, the formulas, a worked example, the mistakes to avoid and a checklist of what you should be able to do.

Download the A4 sheet (PDF)

Key definitions

Frequency: How many times a value or class appears in the data.
Class interval: A group of values in grouped data, such as 10–20.
Bar graph: Bars of equal width whose heights show the frequencies of separate categories.

Key formulas

Mean; weighted mean	\(\bar x=\frac{\sum f_ix_i}{\sum f_i};\) \(\bar x_w=\frac{\sum w_ix_i}{\sum w_i}\)
Combined mean of two groups	\(\frac{n_1\bar x_1+n_2\bar x_2}{n_1+n_2}\)
Mixture concentration	\(\frac{q_1c_1+q_2c_2}{q_1+q_2}\)
Average speed = total distance ÷ total time; 100% stacked bars compare proportions, not totals
Median: middle value in order (\(n\) even: mean of the two middle values); mode: most frequent value

Worked example

A report gives weight \(40\%\) to coursework and \(60\%\) to the exam. Find the result for coursework \(85\) and exam \(70\).

\(0.4 \times 85 + 0.6 \times 70 = 34 + 42 = 76\).

Common mistakes

Averaging two group means without weighting by the group sizes.
Average speed as the mean of the two speeds when the times differ.
Dividing a weighted total by the number of values instead of the sum of the weights.
Comparing totals from a 100% stacked chart: it shows only proportions.

You should be able to…

Find a mean and a weighted mean, combine two group averages and read a stacked bar chart.
Solve mixture and purity questions, correct a mean and use frequency tables.
Answer multi-part problems on class averages, grading schemes and blends.
Find the ratio in which to mix, a missing weight or value, and explain misleading averages.

The printable sheet

Statistics knowledge organiser for CBSE Class 9 Maths: one A4 page of key definitions, formulas, a worked example and common mistakes — Statistics knowledge organiser (CBSE Class 9 Maths), A4. Download the PDF.

Revise it next

Other CBSE Class 9 Maths topics: Number System · Introduction to Polynomials · Sequences and Progressions · Exploring Algebraic Identities · Linear Equations in Two Variables · Coordinate Geometry · Introduction to Euclid's Geometry: Axioms and Postulates · Lines and Angles · Triangles – Congruence Theorems · 4-gons (Quadrilaterals) · Circles · Area and Perimeter · Surface Area and Volume · Introduction to Probability · All CBSE Class 9 Maths organisers