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RRB Group D Standard Deviation & Variance

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This page covers RRB Group D Standard Deviation & Variance with complete concept notes, 3 graded practice MCQs, key points and exam-specific tips. Free to study.

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Concept Notes

Standard Deviation & Variance— Rules & Concept

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Core Concept

Read this first — the foundation of the topic

Standard Deviation and Variance are measures that tell us how spread out data is from the average. Think of them as measuring 'how different' the numbers are from each other. CORE CONCEPT: Imagine you have marks of 5 students: 10, 20, 30, 40, 50. All are spread out widely.

Now imagine: 28, 29, 30, 31, 32. These are clustered tightly around 30. Both have the same average (30), but the spread is different.

Variance and Standard Deviation measure this spread. Variance (σ²) = Average of squared differences from the mean Standard Deviation (σ) = Square root of Variance KEY RULES: 1. Standard Deviation is always non-negative (≥0) 2. If all numbers are identical, SD = 0 3.

Larger SD means more scattered data; smaller SD means data is clustered 4. Standard Deviation is preferred over Variance because it's in the same units as original data

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Formula Block

Memorise — at least one formula appears in every paper

Variance = Σ(x - mean)² / n

Standard Deviation = √Variance

For quick calculation: Variance = (Σx² / n) - (mean)²

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Exam Patterns

What examiners ask — read before attempting PYQs

SSC CGL typically asks: - Calculate SD or Variance from raw data - Compare spread of two datasets - Identify which dataset has more variation - Effect on SD when all values are multiplied or added by a constant SHORTCUT/TRICK: When values are multiplied by k: New SD = k × Original SD When values are added by c: New SD = Original SD (unchanged) This saves calculation time significantly.

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Worked Example

Solve this step-by-step before moving on

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Step 1

Find mean = (2+4+6+8+10)/5 = 30/5 = 6

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Step 2

Find differences from mean: (2-6)=-4, (4-6)=-2, (6-6)=0, (8-6)=2, (10-6)=4

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Step 3

Square differences: 16, 4, 0, 4, 16

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Step 4

Variance = (16+4+0+4+16)/5 = 40/5 = 8

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Step 5

Standard Deviation = √8 = 2.83 (approximately) COMMON MISTAKE: Students forget to divide by n after summing squared differences. They calculate Σ(x-mean)² but stop there—this is NOT variance. You MUST divide by n. Also, many confuse which measure to use; remember SD is more commonly reported in exams because it's interpretable.

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Exam-Specific Tips

Standard Deviation formula: σ = √[Σ(x - μ)² / n], where μ is the arithmetic mean and n is number of observations.
Variance is the square of Standard Deviation: σ² = Variance.
Alternative variance formula for quick calculation: Variance = (Σx² / n) - (mean)².
Property: If each observation is multiplied by constant k, new SD = k × original SD (linear transformation rule).
Property: If constant c is added to each observation, SD remains unchanged (addition does not affect spread).
Standard Deviation of any dataset is always a non-negative value (σ ≥ 0).
Coefficient of Variation (CV) = (SD / Mean) × 100, used to compare variability across different datasets with different means.
For grouped data, class midpoints are used in calculations, and frequency weights are applied in variance formula.

Practice MCQs

Standard Deviation & Variance — Practice Questions

3graded MCQs · easy to hard · full solution & trap analysis

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Practice 1easy

The variance of a dataset is 36. What is the standard deviation of this dataset?

Practice 2medium

The variance of a dataset is 36. If each observation in the dataset is multiplied by 5, what will be the new variance?

Practice 3hard

Two datasets have the same mean of 50. Dataset A has 8 observations with variance 36, and Dataset B has 12 observations with variance 64. If the two datasets are combined into a single dataset, what is the variance of the combined dataset?

60-Second Revision — Standard Deviation & Variance

Formula: Variance = Σ(x-mean)²/n; SD = √Variance. Use quick formula: Variance = (Σx²/n) - (mean)² to save time.
Multiply by k → SD multiplies by k; Add constant c → SD unchanged. Use this trick for transformation questions.
SD=0 only when all values are identical. Higher SD = more scattered; Lower SD = clustered around mean.
Trap: Don't forget to divide by n after summing squared differences—this is the most common error in calculations.
Remember: SD is preferred over Variance in SSC exams because it's in original units and easier to interpret.
For two datasets with same mean: compare SDs to determine which is more variable/consistent.
In exam, if asked 'which dataset varies more?'—calculate or compare SD values; higher SD = more variation.

RRB Group D Standard Deviation & Variance

Standard Deviation & Variance— Rules & Concept

Key Points to Remember

Exam-Specific Tips

Standard Deviation & Variance — Practice Questions

60-Second Revision — Standard Deviation & Variance