For four different population, the number of positive xi values in the population (n), the sum of xi values (Σxi) and sum of squares of xi values (Σxi²) are given as 1 to 4 below. Compute the standard deviation of each population and arrange in ascending order. Choose the correct answer from the options given below:
1.N = 10, Σxi = 450, Σxi² = 24250
2.N = 8, Σxi = 104, Σxi² = 1424
3.N = 5, Σxi = 120, Σxi² = 3600
4.N = 7, Σxi = 28, Σxi² = 140
A1, 2, 3, 4
B2, 4, 1, 3
C4, 2, 3, 1 ✓ Correct
D3, 1, 2, 4
Correct answer: (C) 4, 2, 3, 1
Explanation
Using variance as the mean of squares minus the square of the mean, the standard deviations rank as 4, 2, 3, 1.
Population 4 has mean 4 and variance 20 minus 16, so its standard deviation is 2, the smallest.
Population 2 has mean 13 and variance 178 minus 169, giving a standard deviation of 3.
Population 3 has mean 24 and variance 720 minus 576, giving a standard deviation of 12.
Population 1 has mean 45 and variance 2425 minus 2025, so its standard deviation is 20, the largest.
The formula used is variance equals the mean of squared values minus the square of the mean.
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