Statistics formulas

Every formula JEE Advanced expects you to know for Statistics, with the variables spelled out. Free, no sign-up. Read it before a mock, not during one.

Practise these formulas

Formulas: 30
Subject: Mathematics
Exam: JEE Advanced
No sign-in needed: ₹0

Statistics, every formula

30 formulas, typeset and free. Print it, or keep it open beside your practice.

Class mark (mid value)
$mid value = \frac{lower limit + upper limit}{2}$
Mean (individual series)
$\overset{x}{ˉ} = \frac{1}{n} i = 1 \sum n x_{i}$
Mean (discrete/continuous)
$\overset{x}{ˉ} = \frac{\sum f _{i} x _{i}}{\sum f _{i}} = \frac{1}{N} \sum f_{i} x_{i}$
Assumed-mean method
$\overset{x}{ˉ} = A + \frac{\sum f _{i} ( x _{i} - A )}{N}$
Step-deviation method
$\overset{x}{ˉ} = A + h \times \frac{\sum f _{i} d _{i}}{N}, d_{i} = \frac{x _{i} - A}{h}$
Combined mean
$\overset{x}{ˉ} = \frac{n _{1} x ˉ _{1} + n _{2} x ˉ _{2}}{n _{1} + n _{2}}$
Weighted mean
$\overset{x}{ˉ} = \frac{\sum w _{i} x _{i}}{\sum w _{i}}$
Geometric mean
$G . M . = (x_{1} x_{2} \dots x_{n})^{1/ n}$
Harmonic mean
$H . M . = \frac{n}{\sum \frac{1}{x _{i}}}$
AM ≥ GM ≥ HM
$A . M . \geq G . M . \geq H . M .$
positive values
Sum of deviations from mean
$\sum (x_{i} - \overset{x}{ˉ}) = 0$
Effect of change of origin
$add k to each \Rightarrow mean + k$
E(aX+b)
$E (a X + b) = a E (X) + b$
Median (odd n)
$size of (\frac{n + 1}{2})^{th} item$
Median (even n)
$average of (\frac{n}{2})^{th} and (\frac{n}{2} + 1)^{th}$
Median (continuous)
$Median = l + \frac{h}{f} (\frac{N}{2} - C)$
Mode (continuous)
$Mode = l + \frac{f _{1} - f _{0}}{2 f _{1} - f _{0} - f _{2}} \times h$
Empirical relation
$Mode = 3 Median - 2 Mean$
Range
$Range = Max - Min$
Coefficient of range
$\frac{Max - Min}{Max + Min}$
Mean deviation
$M . D . = \frac{1}{n} \sum ∣ x_{i} - M ∣$
M = mean/median/mode
Coefficient of MD
$\frac{Mean Deviation}{M}$
Quartile deviation
$Q . D . = \frac{Q _{3} - Q _{1}}{2}$
First & third quartiles
$Q_{1} = (\frac{n + 1}{4})^{th}, Q_{3} = 3 (\frac{n + 1}{4})^{th}$
Variance (individual)
$σ^{2} = \frac{1}{n} \sum x_{i}^{2} - (\frac{1}{n} \sum x_{i})^{2}$
Variance (frequency)
$σ^{2} = \frac{1}{N} \sum f_{i} x_{i}^{2} - (\frac{1}{N} \sum f_{i} x_{i})^{2}$
Standard deviation
$σ = σ^{2}$
Coefficient of variation
$C . V . = \frac{σ}{x ˉ} \times 100$
Variance of aX+b
$V (a X + b) = a^{2} V (X)$
Variance of an AP
$σ^{2} = \frac{n ^{2} - 1}{12} d^{2}$
for a, a+d, ..., a+(n-1)d

Know the Statistics formulas. Now use them.

Formulas only stick when you apply them under time. Adaptive practice picks the concept you keep dropping marks on.

Create a free account All formula sheets

Join QuestPix, Today!

Get notified first, with exam & curriculum updates, course & test series launch offers, motivation & success stories and free learning resources recommended by toppers.

Statistics formulas

Statistics, every formula

Class mark (mid value)

Mean (individual series)

Mean (discrete/continuous)

Assumed-mean method

Step-deviation method

Combined mean

Weighted mean

Geometric mean

Harmonic mean

AM ≥ GM ≥ HM

Sum of deviations from mean

Effect of change of origin

E(aX+b)

Median (odd n)

Median (even n)

Median (continuous)

Mode (continuous)

Empirical relation

Range

Coefficient of range

Mean deviation

Coefficient of MD

Quartile deviation

First & third quartiles

Variance (individual)

Variance (frequency)

Standard deviation

Coefficient of variation

Variance of aX+b

Variance of an AP

More JEE Advanced Mathematics formula sheets

Know the Statistics formulas. Now use them.

Join QuestPix, Today!