SSC CGL Statistics – Measures of Dispersion – Exam-Level Drill

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SSC CGL Statistics – Measures of Dispersion – Exam-Level Drill – 10 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.  
Ten values have mean 12 and SD 3. One value equal to 12 is removed. What is the variance of the remaining nine values?

Correct Answer: A [10]

Explanation:

Σx² = 10(9 + 144) = 1530 → 1386; Σx = 108 → mean 12; 1386/9 − 144 = 10.

2.  
A group of 40 values has mean 30 and SD 5. When a second group of 10 values with mean 35 is added, the 50 values have mean 31 and SD 6. What is the SD of the second group?

Correct Answer: B [√60 ≈ 7.75]

Explanation:

50 × 36 = 40(25 + 1) + 10(σ² + 16) → 1800 = 1040 + 10σ² + 160 → σ² = 60 → σ = √60 ≈ 7.75.

3.  

Directions (Q 38–39): Waiting time (minutes) of 50 patients at a fictional clinic.

Minutes 0–10 10–20 20–30 30–40 40–50
Patients 10 9 12 9 10
Data tableWhat is the standard deviation of the waiting time?

Correct Answer: A [14 min]

Explanation:

A = 25, h = 10: Σfu = 0, Σfu² = 98 → σ = 10√(98/50) = 10√1.96 = 14.

4.  
(Use the directions above – Q 38–39)
Data tableWhat is the coefficient of variation of the waiting time?

Correct Answer: C [56%]

Explanation:

Answer: 56%. 14/25 × 100 = 56%.

5.  
For a normal distribution with standard deviation 15, the mean deviation about the mean is approximately:

Correct Answer: B [12]

Explanation:

MD ≈ ⅘ σ = 12 (more precisely 0.798 × 15 ≈ 11.97).

6.  
Twenty observations have mean 6 and SD 2. What is Σx²?

Correct Answer: D [800]

Explanation:

Σx² = n(σ² + x̄²) = 20(4 + 36) = 800.

7.  
Two-quantity comparison
Quantity I: variance of 1, 2, 3, …, 9
Quantity II: variance of 2, 4, 6, 8, 10

Correct Answer: B [Quantity I < Quantity II]

Explanation:

QI = (81 − 1)/12 ≈ 6.67; QII = 4 × (25 − 1)/12 = 8.

8.  
Spot My Mistake“Group A (50 values, SD 4) and group B (50 values, SD 6) have means 20 and 30. Combined SD = (4 + 6)/2 = 5.” What is the correct combined SD?

Correct Answer: C [√51 ≈ 7.14]

Explanation:

Mean 25, d = ±5: σ² = [50(16 + 25) + 50(36 + 25)]/100 = 51.

9.  
Statement-basedWhich of the following is/are correct about the Lorenz curve?
I. The farther the curve lies below the line of equality, the greater the inequality.
II. For perfect equality the Gini coefficient is 1.

Correct Answer: D [Only I]

Explanation:

Perfect equality gives a Gini coefficient of 0, not 1.

10.  
Inclusive classes run from 10–19 to 50–59. Using class boundaries, what is the coefficient of range (to two decimals)?

Correct Answer: B [0.72]

Explanation:

Boundaries 9.5 and 59.5: (59.5 − 9.5)/(59.5 + 9.5) = 50/69 ≈ 0.72.

➤ 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

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