# Statistics Notes, Class 11 Mathematics | SwaVid

Statistics, NCERT Class 11 Mathematics: notes with key ideas, formulas, common mistakes and 3 quick checks with worked answers.

Canonical: https://www.swavid.com/cbse/class-11/maths/chapter/statistics

Source: https://www.swavid.com/cbse/class-11/maths/chapter/statistics

# Statistics

## Formulas and definitions

## Key ideas

## Common mistakes

## Quick checks

## Keep going

## Questions parents ask

## Class 11 Mathematics on SwaVid

### Measures of dispersion

### Mean deviation

### Variance

### Standard deviation

### Shortcut methods for grouped data

### Next chapter

### Related chapter

### All chapters

SwaVid › CBSE › Class 11 › Mathematics › Statistics

Notes written by SwaVid from the NCERT textbook.

Class 11 Mathematics, Chapter 13. Key ideas, formulas and common mistakes.

CBSE does not print marks for a single chapter.

Short answer. This chapter covers measures of dispersion used to quantify the spread of data points around a central value. Students learn to calculate mean deviation, variance, and standard deviation for ungrouped and grouped frequency distributions.

Source: NCERT Mathematics (Reprint 2026-27) , Chapter 13, Statistics

Dispersion measures the degree of scatter of observations around a central tendency. The primary measures studied in this chapter are mean deviation, variance, and standard deviation.

Mean deviation is the arithmetic mean of the absolute values of deviations of observations from a measure of central tendency, usually the mean or the median. Using absolute values ensures that positive and negative deviations do not cancel each other out.

Variance is the arithmetic mean of the squares of deviations of observations from their arithmetic mean. Squaring the deviations eliminates negative signs and penalises larger deviations more heavily.

Standard deviation is the positive square root of the variance. It shares the same unit of measurement as the original observations, making it easier to interpret.

For continuous frequency distributions with equal class intervals, step-deviation methods simplify calculations. Using assumed mean and scale factors reduces the arithmetic needed to find the mean, variance, and standard deviation.

Try each question first. Then tap it to see the answer.

Sum of observations = 4 + 7 + 8 + 9 + 10 + 12 + 13 + 17 = 80

Mean x̄ = 80 / 8 = 10

Absolute deviations |xᵢ - 10|: 6, 3, 2, 1, 0, 2, 3, 7

Sum of absolute deviations = 6 + 3 + 2 + 1 + 0 + 2 + 3 + 7 = 24

M.D.(x̄) = 24 / 8 = 3

3

Mean x̄ = (1 + 2 + 3 + 4 + 5) / 5 = 15 / 5 = 3

Deviations (xᵢ - 3): -2, -1, 0, 1, 2

Squared deviations (xᵢ - 3)²: 4, 1, 0, 1, 4

Sum of squared deviations = 4 + 1 + 0 + 1 + 4 = 10

Variance σ² = 10 / 5 = 2

2

Mean x̄ = (6 + 8 + 10 + 12 + 14) / 5 = 50 / 5 = 10

Squared deviations (xᵢ - 10)²: (-4)² = 16, (-2)² = 4, 0² = 0, 2² = 4, 4² = 16

Sum of squared deviations = 16 + 4 + 0 + 4 + 16 = 40

Variance σ² = 40 / 5 = 8

Standard deviation σ = √8 = 2√2

2√2

Probability .

Sets .

The 14 chapters of Class 11 Mathematics .

The CBSE Class 11 Maths curriculum says it gives no chapter or unit-wise weightage. Theory is 80 marks, plus 20 for internal assessment.

No. They are written by SwaVid from the NCERT textbook. The CBSE curriculum is the reference for what is assessed.

Probability.

SwaVid is an AI tutor for Indian students in Classes 6 to 12. It finds the earlier ideas a child missed, then teaches today’s chapter. Start free to see how it works.

- Ch 13 NCERT book
- 80 marks, theory paper
- 3 quick checks
- Forgetting to take absolute values when finding mean deviation . Always drop the negative sign or take the magnitude |xᵢ - a| of each deviation, because the algebraic sum of deviations from the mean is always zero.
- Confusing variance with standard deviation . Variance is expressed in squared units (σ²). Take the positive square root of variance to obtain the standard deviation (σ).
- Dividing by n instead of N = ∑ fᵢ in grouped data . For frequency distributions, always divide by the total frequency N = ∑ fᵢ, not the number of classes or rows.
- Squaring the class width factor h incorrectly in the step-deviation formula . Remember that variance scales by h², so multiply the bracketed expression by (h² / N²), while standard deviation scales by h, multiplying by (h / N).

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