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Σ = sum of
N = total number of outcomes
Table 4.4 Example 1: Calculating Standard Deviation for Grouped Data
Cost Frequency, f Mid-points, (x) fx x² fx²
0 < 200 8 100 800 10,000 80,000
201 < 400 6 300 1,800 90,000 540,000
401 < 600 10 500 5,000 250,000 2,500,000
601 < 800 4 700 2,800 490,000 1,960,000
Total Σf = 28 Σfx =10,400 840,000 Σfx² = 5,080,000
2
2
= ∑ - ∑ ²
∑ ∑
5,080,000 − 10,400
= √ ²
14 28
= √362,857.14 − 137,959.18
= √224,897.96
= 471.23
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