A student scores the following marks in 5 subjects: 60, 75, 80, 90, 95. What is the standard deviation?
Solution:
Step 1: Find the mean Mean = (60 + 75 + 80 + 90 + 95) ÷ 5 = 400 ÷ 5 = 80
Step 2: Find deviations from mean and their squares
Marks | Deviation (x − 80) | Square |
60 | −20 | 400 |
75 | −5 | 25 |
80 | 0 | 0 |
90 | +10 | 100 |
95 | +15 | 225 |
Sum of squares = 400 + 25 + 0 + 100 + 225 = 750
Step 3: Variance Variance = 750 ÷ 5 = 150
Step 4: Standard deviation SD = √150 ≈ 12.25
Nearest option = 12.5
Correct Answer: (c)
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