Knowledge organisers

Statistics: CBSE Class 11 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

Range: Maximum minus minimum: the simplest measure of spread.
Mean deviation: The average distance of the values from the mean or median.
Standard deviation: The square root of the variance; a larger value means the data are more spread out.

Key formulas

Mean deviation about \(a\)	\(\frac{\sum f_i\|x_i-a\|}{\sum f_i}\)
Variance; SD	\(\sigma^2=\frac{\sum f_i(x_i-\bar x)^2}N=\frac{\sum f_ix_i^2}N-\bar x^2,\) \(\sigma=\sqrt{\sigma^2}\)
Adding \(k\) leaves \(\sigma\) unchanged; multiplying by \(k\) multiplies \(\sigma\) by \(\|k\|\)

Worked example

Find the mean deviation about the mean of \(3, 5, 9, 11\).

\(\bar x = 7\); \(|x - 7| = 4, 2, 2, 4\): MD \(= \dfrac{12}{4} = 3\).

Common mistakes

Dropping the modulus in the mean deviation (the deviations then add to \(0\)).
Using the class limits instead of the class marks for grouped data.
Dividing by \(n\) (number of classes) instead of \(N = \sum f_i\).
Forgetting to take the square root for the standard deviation, or subtracting \(\bar x\) instead of \(\bar x^2\) in the short formula.

You should be able to…

Find the range, a simple mean deviation and a simple variance, and know how SD responds to scaling.
Find mean deviations and variances from frequency tables, including about the median.
Compare the spread of two data sets and interpret the result.
Work backwards from a mean and variance to missing or corrected values.

The printable sheet

Statistics knowledge organiser for CBSE Class 11 Maths: one A4 page of key definitions, formulas, a worked example and common mistakes — Statistics knowledge organiser (CBSE Class 11 Maths), A4. Download the PDF.

Revise it next

Other CBSE Class 11 Maths topics: Sets · Relations and Functions · Trigonometric Functions · Complex Numbers and Quadratic Equations · Linear Inequalities · Permutations and Combinations · Binomial Theorem · Sequences and Series · Straight Lines · Conic Sections · Introduction to Three Dimensional Geometry · Limits and Derivatives · Probability · All CBSE Class 11 Maths organisers