NCERT Class 11 Statistics Notes Chapter 13 – Key Concepts, Formulas & Summary

8 CBSE Marks

★★★★★ Difficulty

7 Topics

Low JEE Weight

Topics Covered

7 key topics in this chapter

Measures of Central Tendency: Mean, Median, Mode

Weighted Mean

Mean Deviation (Ungrouped & Grouped)

Variance & Standard Deviation

Frequency Distribution

Coefficient of Variation

Comparison of Two Series

Study Resources

📖 NCERT Notes ✏️ MCQ Practice ✅ True / False Quiz 📝 Exercise Solutions

𝑓 Key Formulae

Essential mathematical expressions for this chapter — understand derivations, not just results.

Mean (ungrouped)

\[\bar{x} = \dfrac{\sum x_i}{n}\]

📌 Simple arithmetic average

Mean (grouped)

\[\bar{x} = \dfrac{\sum f_i x_i}{\sum f_i}\]

📌 fᵢ = frequency, xᵢ = class midpoint

Mean Deviation

\[MD = \dfrac{\sum f_i|x_i-\bar{x}|}{\sum f_i}\]

📌 Around mean or median

Variance

\[\sigma^2 = \dfrac{\sum f_i(x_i-\bar{x})^2}{\sum f_i}\]

📌 Square of standard deviation

Variance (alt.)

\[\sigma^2 = \dfrac{\sum f_i x_i^2}{N} - \bar{x}^2\]

📌 Computational shortcut; N = Σfᵢ

Std. Deviation

\[\sigma = \sqrt{\sigma^2}\]

📌 Always non-negative

Coeff. of Var.

\[CV = \dfrac{\sigma}{\bar{x}} \times 100\%\]

📌 Dimensionless measure of relative spread

🎯 Exam-Ready Insights

Important points to remember — curated from CBSE Board question patterns.

CBSE 5-mark: given a frequency distribution, find mean and variance — use the shortcut formula to avoid long computation.

Coefficient of Variation (CV) compares consistency: lower CV → more consistent series.

Mean deviation is always calculated around either the mean or median — the question will specify which.

Median of grouped data uses the formula: M = l + [(N/2 − CF)/f]×h — not tested in Class XI but know the idea.

Effect of change of origin/scale: if yᵢ = a + bxᵢ, then σᵧ = |b|·σₓ and ȳ = a + b·x̄.

🏆 Competitive Exam Strategy

Targeted tips for JEE Main, JEE Advanced, NEET, BITSAT, and KVPY.

JEE Main

JEE Main tests "variance of n natural numbers = (n²−1)/12" and "mean of squares" — derive these from the general formula.

JEE Main

Changing all observations: adding a constant does NOT change variance; multiplying by a constant k multiplies variance by k².

BITSAT

BITSAT asks combined mean and variance of two groups — use the combined mean formula and then recalculate combined variance.

NEET

In NEET Biology (Biostatistics), mean and standard deviation describe experimental data distributions — understand the biological context.

⚠️ Common Mistakes to Avoid

Using n in the denominator when the data is grouped — use N = Σfᵢ instead.

Forgetting the absolute value bars in the mean deviation formula.

Computing variance as Σ(xᵢ−x̄)/n (without squaring) — always square the deviations.

Confusing mean deviation with standard deviation — they use different formulas.

💡 Key Takeaways

◆

Mean measures central tendency; standard deviation measures spread around the mean.

◆

Variance = (Standard Deviation)²; SD is preferred as it has the same unit as data.

◆

Coefficient of Variation is used to compare two series with different units or scales.

◆

Mean Deviation is always ≥ 0; it equals 0 only when all observations are identical.

◆

A larger standard deviation means greater variability — data points are spread further from the mean.

Statistics