Consider the data set: 4, 8, 6, 5, 3, 9. Find the variance.
\(\\dfrac{161}{36}\)
Mean \(\\mu = \\dfrac{4+8+6+5+3+9}{6} = \\dfrac{35}{6}\).
Sum of squares: \(4^2+8^2+6^2+5^2+3^2+9^2 = 16+64+36+25+9+81 = 231\).
Variance \(= \\dfrac{\\sum x_i^2}{n} - \\mu^2 = \\dfrac{231}{6} - \\left(\\dfrac{35}{6}\\right)^2 = \\dfrac{1386 - 1225}{36} = \\dfrac{161}{36}\).
Hence, the variance is \(\\dfrac{161}{36}\).
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Important Questions from Elementary Statistics
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A. 5 and 5
B. 3 and 5
C. 5 and 4
D. 3 and 4
For which set of numbers do the mean, median and mode all have the same value?
The median of 5, 8, 25, 22, 34, 18 is
Find the mean of first 5 two-digit multiples of 4.
