SSC CGL Statistics – Measures of Dispersion – Level 2 · Exam Level · Paper II Sprint

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SSC CGL Statistics – Measures of Dispersion – Level 2 · Exam Level · Paper II Sprint – 15 questions, subject: Statistics (Tier II Paper II). Every question has the correct answer with a one-line explanation; tap "Show Answer". Free practice for TNPSC, UPSC, SSC, Bank and RRB exams – Shanmugam IAS Academy, Coimbatore.

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1.  
What is the standard deviation of the first 10 natural numbers (correct to two decimals)?

Correct Answer: C [2.87]

Explanation:

√((n² − 1)/12) = √(99/12) = √8.25 ≈ 2.87.

2.  
What is the mean deviation about the mean of 6, 8, 10, 12, 14?

Correct Answer: D [2.4]

Explanation:

Mean 10; deviations 4, 2, 0, 2, 4 → 12/5 = 2.4.

3.  
For 10 observations, Σx = 60 and Σx² = 440. What is the variance?

Correct Answer: A [8]

Explanation:

Answer: 8. 44 − 6² = 8.

4.  
The standard deviation of x is 4. If y = 3x − 7, what is the variance of y?

Correct Answer: B [144]

Explanation:

Answer: 144. Var(y) = 3² × 16 = 144.

5.  
Four workers have mean daily output and SD: P (60, 15), Q (50, 10), R (80, 24), S (40, 9). Who is the most consistent?

Correct Answer: D [Q]

Explanation:

CVs: 25%, 20%, 30%, 22.5% → Q has the lowest CV.

6.  
Two groups of 20 each have means 30 and 34 and SDs 3 and 9. What is the SD of the combined group of 40?

Correct Answer: B [7]

Explanation:

Mean 32; d = ±2 → σ² = [20(9 + 4) + 20(81 + 4)]/40 = 49 → 7.

7.  

Directions (Q 19–21): Marks x and number of students f.

x 10 20 30 40 50
f 1 4 6 4 1
Data tableWhat is the standard deviation?

Correct Answer: C [10]

Explanation:

Mean 30; Σf(x − 30)² = 400 + 400 + 0 + 400 + 400 = 1600 → σ² = 100 → σ = 10.

8.  
(Use the directions above – Q 19–21)
Data tableWhat is the coefficient of variation?

Correct Answer: A [33.33%]

Explanation:

Answer: 33.33%. 10/30 × 100 = 33.33%.

9.  
(Use the directions above – Q 19–21)
Data tableUsing the (N + 1) rule, what is the quartile deviation?

Correct Answer: B [10]

Explanation:

Q₁ = 4.25th item = 20, Q₃ = 12.75th item = 40 → QD = 10.

10.  
Two-quantity comparisonFor the data 2, 4, 6, 8, 10:
Quantity I: standard deviation
Quantity II: mean deviation about the mean

Correct Answer: A [Quantity I > Quantity II]

Explanation:

QI = √8 ≈ 2.83; QII = 12/5 = 2.4.

11.  
Assertion–Reason
A: The coefficient of variation of a series changes if 10 is added to every value.
R: Adding a constant changes the mean but not the standard deviation.

Correct Answer: A [Both A and R are true and R explains A]

Explanation:

CV = σ/x̄: σ is unchanged but x̄ rises by 10, so CV falls.

12.  
Odd one outwhich of these measures is NOT based on all the observations?

Correct Answer: C [Quartile deviation]

Explanation:

Answer: Quartile deviation. QD uses only Q₁ and Q₃.

13.  
Fill in the blankFor a normal distribution, the quartile deviation is about ______ of the standard deviation.

Correct Answer: D [two-thirds]

Explanation:

Answer: two-thirds. QD ≈ 0.674σ ≈ ⅔σ (MD ≈ ⅘σ).

14.  
Reverse questionthe coefficient of variation of a series is 20% and its mean is 45. What is its standard deviation?

Correct Answer: D [9]

Explanation:

Answer: 9. σ = 20 × 45/100 = 9.

15.  
Spot My Mistake“Series A has CV 30% and series B has CV 25%. A has the larger mean, so A is more consistent.” Which series is more consistent?

Correct Answer: B [Series B]

Explanation:

Consistency is judged by the lower CV, whatever the means: B (25%).

➤ Full notes, shortcuts and every answer explained – SSC CGL 2026 Statistics (Tier II Paper II) book (₹149): www.shanmugamiasacademy.in/study-materials/ssc-cgl-statistics

📘 SSC CGL 2026 – Statistics (Tier II Paper II)
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