ZE
ZESTEXAM

Agniveer Army CEE Standard Deviation & Variance

Study Material · Concept Notes · Shortcuts

This page covers Agniveer Army CEE Standard Deviation & Variance with complete concept notes, 8 graded practice MCQs, key points and exam-specific tips. Free to study.

0 PYQs
none yet
8 Practice
MCQs
6 Key Points
to remember
Free
no login needed
Take Free Mock →Full Practice Set
Also for:NDACDSAgniveerCAPF
PYQs
0
Practice
8
Key Points
6
Access
Free
Concept Notes

Standard Deviation & Variance— Rules & Concept

Core ConceptRead 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

Formula BlockMemorise — 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
Exam PatternsWhat 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.

Worked ExampleSolve this step-by-step before moving on
1
Step 1

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

2
Step 2

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

3
Step 3

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

4
Step 4

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

5
Step 5

Standard Deviation = √8 = 2.83 (approximately)

Exam TrapsCommon mistakes students make — avoid these

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.

Key Points to Remember

  • Variance measures average squared distance of data points from the mean; Standard Deviation is its square root.
  • Formula: Variance = Σ(x - mean)² / n; SD = √Variance
  • If all data values are identical, Standard Deviation = 0 (no spread).
  • When multiplying all values by k: New SD = k × Original SD; when adding c: SD remains unchanged.
  • Standard Deviation is preferred in exams because it's expressed in the same units as original data, making it more interpretable.
  • Larger SD indicates data is spread out; smaller SD indicates data is clustered around the mean.

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

8graded MCQs · easy to hard · full solution & trap analysis

All MCQs →
Practice 1easy

The variance of the dataset {2, 4, 6, 8, 10} is:

Practice 2easy

If the standard deviation of a set of numbers is 5, what is the variance?

Practice 3easy

The variance of {5, 5, 5, 5, 5} is:

Practice 4medium

The marks obtained by 5 students in a test are: 10, 20, 30, 40, 50. What is the variance of these marks?

Practice 5medium

If the standard deviation of a dataset is 8, what is the variance?

Practice 6medium

Two datasets have standard deviations of 5 and 10 respectively. Which dataset has greater variability?

Practice 7medium

The variance of the dataset 6, 6, 6, 6, 6 is:

Practice 8hard

The variance of a dataset is 36. What is the standard deviation of this 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.
←Mean, Median, ModeProbability→
Studied the notes? Now test yourself
See how Standard Deviation & Variance appears in the real Agniveer Army CEE paper
Full timed mock · Instant All-India percentile · Free
Start Free Mock →Practice Panel
✓ Free forever for basic prep✓ No app download✓ Real exam-pattern questions✓ 12,000+ aspirants
Test Standard Deviation & Variance under exam conditions
Free Agniveer Army CEE mock · instant rank · no login
Free Mock →
Agniveer Army CEE Standard Deviation & Variance — Study Material & 8 Practice MCQs | ZestExam