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ch3measuresofvariability

# We shall derive a practical formula for practical i 2

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Unformatted text preview: t, at the end, the trouble of rounding will appear. It would be useful to derive another formula that does not call upon µ until a very late stage. We shall derive a practical formula for σ . practical i 2 2 ( x1 − µ) 2 = x1 − 2 µx1 + µ2 2 ( x N − µ) 2 = x N − 2 µx N + µ2 _____________________________ ( xi − µ) 2 = ∑xi2 − 2 µ∑xi + Nµ2 ∑ Now, x µ=∑ i N , so that ∑ x = Nµ i ∴ ∑ ( xi − µ ) 2 = ∑ xi2 − 2 µ ( Nµ ) + Nµ 2 = ∑ xi2 − Nµ 2 ∴σ = ( xi − µ ) 2 ∑ N = xi2 ∑ N − µ 2 →(2) Example 3: Use formula (2) to compute Use σ for set A. Solution 1: Solution 15.2 xi xi2 9.2 6.7 12.4 20.5 ∑x i 231.04 84.64 44.89 153.76 420.25 ∑ x 2 i N =5 ∑x i ∑x 2 i ∑x µ= i = 64 = 934.58 σ= N 64 = 5 = 12.8 = ∑x 2 i N = 64 = 934.58 − µ2 934.58 −12.8 2 5 = 186.916 −163.84 = 4.8037 Computer steps: Computer For Company A data ON MODE COMP (1) MODE SD (4) 15.2 DT 9.2 DT 6.7 DT 12.4 DT 20.5 DT 15.2 SHIFT SHIFT SHIFT SHIFT S-SUM n (3) EXE S-SUM ∑ x (2) EXE S-SUM ∑ x 2 (1) EXE SHIFT S-VAR SHIFT S-VAR x xσn (1) EXE (2) EXE 5 64 934.58 12.8 4.803748536...
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