The salary in rupees of 10 employees in a company per day is 50, 55, 60, 65,…
2023
The salary in rupees of 10 employees in a company per day is 50, 55, 60, 65, 70, 72, 75, 80, 84, 89.What is the standard deviation in the above data?
- A.
13.751
- B.
11.983
- C.
9.432
- D.
5.754
Attempted by 23 students.
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Correct answer: B
Key insight: Use the population standard deviation formula σ = sqrt(Σ(xi − μ)² / N).
Step 1: Compute the mean μ = (50 + 55 + 60 + 65 + 70 + 72 + 75 + 80 + 84 + 89) / 10 = 700 / 10 = 70.
Step 2: Compute squared deviations: (50−70)² = 400, (55−70)² = 225, (60−70)² = 100, (65−70)² = 25, (70−70)² = 0, (72−70)² = 4, (75−70)² = 25, (80−70)² = 100, (84−70)² = 196, (89−70)² = 361. Sum = 1436.
Step 3: Variance = 1436 / 10 = 143.6. Standard deviation σ = sqrt(143.6) = 11.983 (approximately 11.98).
Therefore the standard deviation of the given data (population formula) is 11.983.