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Statistics formula sheet

Every formula in the Statistics chapter for JEE Main, with one line on when it applies. Topic 1 is open to everyone; sign in free to read all 13 and download the PDF.

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How we count: 7× asked means 7 past JEE Main questions in the PrepWiser bank needed that formula, and "last" is the latest year one appeared. ★ marks formulas asked 8 or more times.

Measures of central tendency

Mean (step deviation)
10× asked, last 2026
xˉ=∑fixiN=A+h ∑fiuiN,ui=xi−Ah\bar x=\frac{\sum f_ix_i}N=A+h\,\frac{\sum f_iu_i}N,\qquad u_i=\frac{x_i-A}h
xix_i: class mid-point, N=∑fiN=\sum f_i. Frequencies nCr{}^nC_r: ∑r nCr=n2n−1\sum r\,{}^nC_r=n2^{n-1}.
Median
10× asked, last 2026
M=l+N/2−Cf×hM=l+\frac{N/2-C}f\times h
CC: cf before the median class. Ungrouped: middle value (mean of two middles if nn even).
Mode
1× asked, last 2025
Z=l+f1−f02f1−f0−f2×hMode≈3 Median−2 Mean\begin{aligned}&Z=l+\frac{f_1-f_0}{2f_1-f_0-f_2}\times h\\&\text{Mode}\approx3\,\text{Median}-2\,\text{Mean}\end{aligned}
Ungrouped: most frequent value; ties give several modes. The relation needs moderate skew.

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10 more formulas in 3 topics

Mean deviation, Variance and standard deviation and Combined groups and corrected data. Read the first part free. Sign in free with Google to read the rest and download the PDF.

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Mean deviation

  • Mean deviation12×
  • MD of 1, 2, …, n3×

Variance and standard deviation

  • Variance13×
  • About another point9×
  • Step deviations7×
  • 1, …, n and APs8×
  • y = ax + b10×

Combined groups and corrected data

  • Combined mean and variance15×
  • Correcting observations15×
  • Two missing observations23×

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