SSC CGL Quant – Statistics & Probability – Tier II Level · Marathon

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SSC CGL Quant – Statistics & Probability – Tier II Level · Marathon – 9 questions, subject: Quantitative Aptitude. 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.  
The standard deviation of the first 7 natural numbers is:

Correct Answer: D [2]

Explanation:

Variance (n² − 1)/12 = 48/12 = 4 → SD 2.

2.  
The mean of a variable x is 10 and its standard deviation is 3. If y = 2x − 5, the standard deviation of y is:

Correct Answer: B [6]

Explanation:

Subtracting 5 does nothing to SD; multiplying by 2 doubles it → 6.

3.  
A card is drawn from a pack of 52. The probability that it is a red card or a king is:

Correct Answer: A [7/13]

Explanation:

Red 26 + kings 4 − red kings 2 = 28 → 28/52 = 7/13.

4.  
The probability that a leap year chosen at random has 53 Sundays is:

Correct Answer: D [2/7]

Explanation:

366 days = 52 weeks + 2 days; the 2 extra days are one of 7 equally likely pairs, 2 of which contain a Sunday.

5.  
For a moderately skewed distribution the mean is 30 and the median is 28. Using the empirical relation Mode = 3 Median − 2 Mean, the mode is:

Correct Answer: C [24]

Explanation:

3 × 28 − 2 × 30 = 84 − 60 = 24.

6.  
A die is thrown three times. The probability of getting at least one six is:

Correct Answer: D [91/216]

Explanation:

Complement Door: 1 − (5/6)³ = 1 − 125/216 = 91/216.

7.  
The mean of 50 observations was 36. Two observations, 41 and 39, were wrongly entered as 14 and 26. The correct mean is:

Correct Answer: B [36.8]

Explanation:

Sum rises by (41 + 39) − (14 + 26) = 40 → 36 + 40/50 = 36.8.

8.  
The median of the first 20 even natural numbers is:

Correct Answer: C [21]

Explanation:

2, 4, …, 40: middle two are 20 and 22 → 21.

9.  
A box has 15 bulbs of which 5 are defective. Two bulbs are drawn one after another without replacement. The probability that both are good is:

Correct Answer: A [3/7]

Explanation:

10/15 × 9/14 = 90/210 = 3/7.

➤ Full notes, shortcuts and every answer explained – SSC CGL 2026 Quantitative Aptitude book (₹149): www.shanmugamiasacademy.in/study-materials/ssc-cgl-quantitative-aptitude

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