Statistics formulas
Master Statistics through 30 JEE Advanced-level formulas, systematically structured with every variable spelled out. Revise concept-wise, identify the areas where you need improvement, and focus your preparation with greater precision.
Statistics, every formula
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Class mark (mid value)
Q1NumericalClass markThe mid value of the class $10\text{–}20$ is:Mean (individual series)
Q1NumericalMean individualThe mean of $2,4,6,8,10$ is:Mean (discrete/continuous)
Q1NumericalMean discreteFor values $1,2,3$ with frequencies $2,3,5$, the mean is (as a decimal):Assumed-mean method
Q1MCQAssumed meanThe assumed-mean formula for the mean is:- A$A+\dfrac{\sum f_i(x_i-A)}{N}$
- B$\dfrac{\sum f_ix_i}{N}$
- C$A\cdot N$
- D$\dfrac{A}{N}$
- A
Step-deviation method
Q1MCQStep deviationIn the step-deviation method, $d_i$ equals:- A$\dfrac{x_i-A}{h}$
- B$x_i-A$
- C$\dfrac{x_i}{h}$
- D$x_i-\bar x$
- A
Combined mean
Q1NumericalCombined meanTwo groups of sizes $2$ and $3$ have means $10$ and $20$. The combined mean is:Weighted mean
Q1NumericalWeighted meanValues $2,4$ with weights $1,3$ have weighted mean:Geometric mean
Q1NumericalGMThe geometric mean of $2$ and $8$ is:Harmonic mean
Q1NumericalHMThe harmonic mean of $2$ and $6$ is:AM ≥ GM ≥ HM
positive values
Q1MCQAM-GM-HMFor positive numbers, the correct ordering is:- A$A.M.\ge G.M.\ge H.M.$
- B$H.M.\ge G.M.\ge A.M.$
- C$G.M.\ge A.M.\ge H.M.$
- Dall equal
- A
Sum of deviations from mean
Q1NumericalSum of deviationsThe sum $\sum(x_i-\bar x)$ for any data set is:Effect of change of origin
Q1MCQChange of originIf each observation increases by $5$, the mean:- Aincreases by $5$
- Bstays the same
- Cincreases by $25$
- Dhalves
- A
E(aX+b)
Q1NumericalE(aX+b)If $E(X)=4$, then $E(2X+3)$ is:Median (odd n)
Q1NumericalMedian oddThe median of $3,1,4,1,5$ (sorted $1,1,3,4,5$) is:Median (even n)
Q1NumericalMedian evenThe median of $2,4,6,8$ is:Median (continuous)
Q1MCQMedian continuousThe continuous-series median formula is:- A$l+\dfrac{h}{f}\left(\dfrac{N}{2}-C\right)$
- B$l+\dfrac{f}{h}\left(\dfrac{N}{2}-C\right)$
- C$\dfrac{N}{2}$
- D$l+\dfrac{h}{f}\cdot N$
- A
Mode (continuous)
Q1MCQMode continuousThe continuous-series mode formula is:- A$l+\dfrac{f_1-f_0}{2f_1-f_0-f_2}\times h$
- B$3\text{Median}-2\text{Mean}$
- C$l+\dfrac{N}{2}$
- D$\dfrac{f_1-f_0}{h}$
- A
Empirical relation
Q1NumericalEmpirical relationIf Mean $=20$ and Median $=22$, then Mode $=3\,$Median$-2\,$Mean equals:Range
Q1NumericalRangeThe range of $4,8,15,16,23,42$ is:Coefficient of range
Q1MCQCoefficient of rangeThe coefficient of range is:- A$\dfrac{\text{Max}-\text{Min}}{\text{Max}+\text{Min}}$
- B$\text{Max}-\text{Min}$
- C$\dfrac{\text{Max}+\text{Min}}{2}$
- D$\dfrac{\text{Min}}{\text{Max}}$
- A
Mean deviation
M = mean/median/mode
Q1NumericalMean deviationThe mean deviation of $2,4,6$ about their mean $4$ is:Coefficient of MD
Q1MCQCoefficient of MDThe coefficient of mean deviation is:- A$\dfrac{\text{Mean Deviation}}{M}$
- B$\text{M.D.}\times M$
- C$\dfrac{M}{\text{M.D.}}$
- D$\text{M.D.}-M$
- A
Quartile deviation
Q1NumericalQuartile deviationIf $Q_1=10$ and $Q_3=30$, the quartile deviation is:First & third quartiles
Q1MCQQuartiles$Q_1$ is the size of the:- A$\left(\dfrac{n+1}{4}\right)^{\text{th}}$ item
- B$\left(\dfrac{n+1}{2}\right)^{\text{th}}$ item
- C$\left(\dfrac{3(n+1)}{4}\right)^{\text{th}}$ item
- D$n$th item
- A
Variance (individual)
Q1NumericalVarianceThe variance of $2,4,6$ (mean $4$) is:Variance (frequency)
Q1MCQVariance frequencyThe frequency-series variance is:- A$\dfrac{1}{N}\sum f_ix_i^{2}-\left(\dfrac{1}{N}\sum f_ix_i\right)^{2}$
- B$\dfrac{1}{N}\sum f_ix_i$
- C$\sum f_ix_i^{2}$
- D$\left(\dfrac{1}{N}\sum f_ix_i\right)^{2}$
- A
Standard deviation
Q1NumericalStandard deviationIf the variance is $25$, the standard deviation is:Coefficient of variation
Q1NumericalCoefficient of variationIf $\sigma=4$ and $\bar x=20$, the coefficient of variation is:Variance of aX+b
Q1NumericalVariance of aX+bIf $V(X)=3$, then $V(2X+5)$ is:Variance of an AP
for a, a+d, ..., a+(n-1)d
Q1MCQVariance of APThe variance of the AP $a,a+d,\dots,a+(n-1)d$ is:- A$\dfrac{n^{2}-1}{12}d^{2}$
- B$\dfrac{n^{2}-1}{6}d^{2}$
- C$\dfrac{n^{2}}{12}d^{2}$
- D$\dfrac{n-1}{2}d$
- A
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