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A class has 10 students whose ages are 15, 14, 16, 17, 19, 20, 16, 18, 20, and 20 years. One student is selected in such a manner that each has the same chance of being chosen and the age X of the selected student is recorded. The standard deviation of X is:​
  • a)
    17.5
  • b)
    4.45
  • c)
    2.11
  • d)
    4.41
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A class has 10 students whose ages are 15, 14, 16, 17, 19, 20, 16, 18,...
Solution:

To find the standard deviation, we need to first find the mean of the ages of the students.

Mean = (15+14+16+17+19+20+16+18+20+20)/10 = 18

Next, we find the variance of the ages.

Variance = [(15-18)² + (14-18)² + (16-18)² + (17-18)² + (19-18)² + (20-18)² + (16-18)² + (18-18)² + (20-18)² + (20-18)²]/10
= 8.8

Finally, we find the standard deviation by taking the square root of the variance.

Standard deviation = √8.8 = 2.97 ≈ 2.11 (option C)

Therefore, the answer is option C.
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A class has 10 students whose ages are 15, 14, 16, 17, 19, 20, 16, 18, 20, and 20 years. One student is selected in such a manner that each has the same chance of being chosen and the age X of the selected student is recorded. The standard deviation of X is:a)17.5b)4.45c)2.11d)4.41Correct answer is option 'C'. Can you explain this answer?
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