Knowledge organisers

Statistics: CBSE Class 10 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

Class mark: The mid-point of a class interval, used as its representative value.
Modal class: The class with the highest frequency.
Cumulative frequency: The running total of frequencies up to the end of each class.

Key formulas

Class mark	\(x_i=\frac{\text{upper}+\text{lower limit}}2\)
Mean: direct	\(\bar x=\frac{\sum f_ix_i}{\sum f_i}\)
Assumed mean, \(d_i=x_i-a\)	\(\bar x=a+\frac{\sum f_id_i}{\sum f_i}\)
Step deviation, \(u_i=\frac{x_i-a}h\)	\(\bar x=a+\frac{\sum f_iu_i}{\sum f_i}\times h\)
Mode	\(l+\frac{f_1-f_0}{2f_1-f_0-f_2}\times h\)
Median	\(l+\frac{\frac n2-cf}{f}\times h\)
Empirical relation	\(3\,\text{Median}=\text{Mode}+2\,\text{Mean}\)

Worked example

Classes 10–20, 20–30, 30–40, 40–50 with \(f=3,5,8,4\). With \(a=35\) and \(h=10\): \(u=-2,-1,0,1\) and \(\sum fu=-6-5+0+4=-7\), \(n=20\). Mean \(=35+10\left(\frac{-7}{20}\right)=31.5\).

Common mistakes

Using the cf of the median class itself instead of the class before it.
Taking \(f_0,f_2\) from the wrong classes, or using the class with the largest cf as the modal class.
Applying the formulas to non-continuous classes (1–10, 11–20, …). First convert them to 0.5–10.5, 10.5–20.5, …
Forgetting to multiply by \(h\) in the step-deviation method.

You should be able to…

Find the mean of grouped data and pick out the modal class correctly.
Use the step-deviation method, the mode formula and the median formula with a full table.
Write 5-mark answers with the complete table, find missing frequencies and use the empirical relationship.
Handle inclusive classes, two unknown frequencies and questions that combine mean, median and mode.

The printable sheet

Statistics knowledge organiser for CBSE Class 10 Maths: one A4 page of key definitions, formulas, a worked example and common mistakes — Statistics knowledge organiser (CBSE Class 10 Maths), A4. Download the PDF.

Revise it next

Other CBSE Class 10 Maths topics: Real Numbers · Polynomials · Pair of Linear Equations in Two Variables · Quadratic Equations · Arithmetic Progressions · Triangles · Coordinate Geometry · Introduction to Trigonometry · Some Applications of Trigonometry · Circles · Areas Related to Circles · Surface Areas and Volumes · Probability · All CBSE Class 10 Maths organisers