SSC CGL Statistics – Measures of Central Tendency & Partition Values – Exam-Level Drill

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SSC CGL Statistics – Measures of Central Tendency & Partition Values – 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.  
Classes 0–20, 20–40, 40–60, 60–80, 80–100 have frequencies 5, x, 15, y, 5. N = 50 and the mean is 52. Find x and y.

Correct Answer: C [x = 10, y = 15]

Explanation:

x + y = 25 and 1250 + 30x + 70y = 2600 → x = 10, y = 15.

2.  
Classes 0–10, 10–20, 20–30, 30–40, 40–50 have frequencies 8, x, 16, y, 6. N = 50 and the median is 25. Find x and y.

Correct Answer: A [x = 9, y = 11]

Explanation:

25 = 20 + (25 − 8 − x)/16 × 10 → x = 9; y = 50 − 39 = 11.

3.  
The arithmetic mean of two numbers is 25 and their geometric mean is 15. The numbers are:

Correct Answer: C [45 and 5]

Explanation:

25 ± √(625 − 225) = 25 ± 20 → 45 and 5.

4.  
Three groups of 20, 30 and 50 students have means 40, 50 and m. The combined mean is 52. Find m.

Correct Answer: D [58]

Explanation:

5200 = 800 + 1500 + 50m → m = 58.

5.  
The mean of 20 values is 45. If the value 64 is removed, what is the mean of the remaining values?

Correct Answer: A [44]

Explanation:

Answer: 44. (900 − 64)/19 = 836/19 = 44.

6.  
The average age of an 8-member committee is the same today as it was 4 years ago, because one old member has been replaced by a younger one. How much younger is the new member than the one replaced?

Correct Answer: B [32 years]

Explanation:

Total should have risen by 8 × 4 = 32 but did not → the new member is 32 years younger.

7.  
What is the geometric mean of 2, 4, 8, 16, 32?

Correct Answer: C [8]

Explanation:

Product = 2¹⁵ → fifth root = 2³ = 8.

8.  
What is the harmonic mean of 1, 1/2, 1/3, …, 1/9?

Correct Answer: D [1/5]

Explanation:

H = 9 ÷ (1 + 2 + … + 9) = 9/45 = 1/5.

9.  
Two-quantity comparisonclasses 10–20, 20–30, 30–40, 40–50, 50–60, 60–70 have frequencies 8, 12, 25, 30, 15, 10.
Quantity I: Q₃ − median
Quantity II: median − Q₁

Correct Answer: B [Quantity I < Quantity II]

Explanation:

N = 100: Q₁ = 30 + (25 − 20)/25 × 10 = 32, median = 40 + (50 − 45)/30 × 10 = 41⅔, Q₃ = 40 + (75 − 45)/30 × 10 = 50 → QI = 8⅓ < QII = 9⅔.

10.  
Statement-basedFor two unequal positive numbers, which of the following is/are correct?
I. AM × HM = GM²
II. AM > GM > HM
III. HM > GM

Correct Answer: A [Only I and II]

Explanation:

AM × HM = ab = GM²; for unequal numbers AM > GM > HM, so III is false.

➤ 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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