SSC CGL Statistics – Measures of Dispersion – Level 3 · Challenge
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Answer: 38%. 100% − 62% = 38%.
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SSC CGL Statistics – Measures of Dispersion – Level 3 · Challenge – 8 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.
Nine values have mean 20 and SD 4. A tenth value equal to 20 is added. What is the new variance?
Correct Answer: C [14.4]
Explanation:
Mean stays 20; Σ(x − 20)² stays 9 × 16 = 144 → 144/10 = 14.4.
2.
Diagram-basedThe box plots show the marks of a fictional class in two subjects (Maths: min 20, Q₁ 35, median 48, Q₃ 60, max 85; Science: min 30, Q₁ 42, median 50, Q₃ 58, max 70).
What is the difference between the quartile deviations of Maths and Science?
What is the difference between the quartile deviations of Maths and Science?
Correct Answer: A [4.5]
Explanation:
QD(M) = 25/2 = 12.5; QD(S) = 16/2 = 8 → difference 4.5.
3.
25 observations have mean 50 and SD 6. One value 40 was read as 65. What is the correct variance?
Correct Answer: D [30]
Explanation:
Σx 1250 → 1225 (mean 49); Σx² 63,400 → 63,400 − 4,225 + 1,600 = 60,775 → 2,431 − 2,401 = 30.
4.
What is the variance of 3, 7, 11, 15, …, 43?
Correct Answer: B [160]
Explanation:
AP: n = 11, d = 4 → 16 × (121 − 1)/12 = 160.
5.
Two numbers have mean 15 and standard deviation 3. The numbers are:
Correct Answer: A [12 and 18]
Explanation:
For two numbers σ = half the difference → difference 6 → 15 ± 3.
6.
True/False countHow many of the following statements are true?
(i) The SD is never less than the mean deviation about the mean.
(ii) If all values are equal, the SD is zero.
(iii) The variance of 2x is twice the variance of x.
(iv) The quartile deviation can be found for a distribution with open-end classes.
(i) The SD is never less than the mean deviation about the mean.
(ii) If all values are equal, the SD is zero.
(iii) The variance of 2x is twice the variance of x.
(iv) The quartile deviation can be found for a distribution with open-end classes.
Correct Answer: C [Three]
Explanation:
(i), (ii), (iv) true; Var(2x) = 4 Var(x).
7.
The mean of x is 50 and its CV is 20%. If y = 2x + 10, what is the CV of y (to two decimals)?
Correct Answer: D [18.18%]
Explanation:
σx = 10 → σy = 20; ȳ = 110 → 20/110 × 100 ≈ 18.18%.
8.
In a Lorenz chart, the bottom 80% of households of a fictional town together get 62% of the total income. What share do the top 20% get?
Correct Answer: C [38%]
Explanation:
Answer: 38%. 100% − 62% = 38%.
➤ 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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