Dataset

Data: 11,15,11,16,12,17,13,21,14,21,15,22

Find the dispersion of a given dataset.

Final Answer:

s = 13.8889

S = 11 + 15 + 11 + 16 + 12 + 17 + 13 + 21 + 14 + 21 + 15 + 22 = 188 m = S / 12 = 188 / 12 = \frac{4 7}{3} = 15 \frac{2}{3} ≐ 15.6667 s_{1} = (m - 11)^{2} = (15.6667 - 11)^{2} = \frac{1 9 6}{9} = 21 \frac{7}{9} ≐ 21.7778 s_{2} = (m - 15)^{2} = (15.6667 - 15)^{2} = \frac{4}{9} ≐ 0.4444 s_{3} = (m - 11)^{2} = (15.6667 - 11)^{2} = \frac{1 9 6}{9} = 21 \frac{7}{9} ≐ 21.7778 s_{4} = (m - 16)^{2} = (15.6667 - 16)^{2} = \frac{1}{9} ≐ 0.1111 s_{5} = (m - 12)^{2} = (15.6667 - 12)^{2} = \frac{1 2 1}{9} = 13 \frac{4}{9} ≐ 13.4444 s_{6} = (m - 17)^{2} = (15.6667 - 17)^{2} = \frac{1 6}{9} = 1 \frac{7}{9} ≐ 1.7778 s_{7} = (m - 13)^{2} = (15.6667 - 13)^{2} = \frac{6 4}{9} = 7 \frac{1}{9} ≐ 7.1111 s_{8} = (m - 21)^{2} = (15.6667 - 21)^{2} = \frac{2 5 6}{9} = 28 \frac{4}{9} ≐ 28.4444 s_{9} = (m - 14)^{2} = (15.6667 - 14)^{2} = \frac{2 5}{9} = 2 \frac{7}{9} ≐ 2.7778 s_{10} = (m - 21)^{2} = (15.6667 - 21)^{2} = \frac{2 5 6}{9} = 28 \frac{4}{9} ≐ 28.4444 s_{11} = (m - 15)^{2} = (15.6667 - 15)^{2} = \frac{4}{9} ≐ 0.4444 s_{12} = (m - 22)^{2} = (15.6667 - 22)^{2} = \frac{3 6 1}{9} = 40 \frac{1}{9} ≐ 40.1111 s = (s_{1} + s_{2} + s_{3} + s_{4} + s_{5} + s_{6} + s_{7} + s_{8} + s_{9} + s_{10} + s_{11} + s_{12}) / 12 = (21.7778 + 0.4444 + 21.7778 + 0.1111 + 13.4444 + 1.7778 + 7.1111 + 28.4444 + 2.7778 + 28.4444 + 0.4444 + 40.1111) / 12 = 13.8889

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