Use of summation notation
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The document discusses summation notation and provides examples of calculating the mean using summation notation. It gives examples of calculating the sum, mean, variance, and using summation to find the mean of data sets where the values are a certain number away from a given value. It provides step-by-step workings for calculating the mean when the values are 100 above their actual values.
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Use of summation notation
- 2. Use of summation notation (∑) First to understand = + + = + + = Formula For Mean = ∑ Example-1. A data set contains the observations 2, 1, 3, 2, 3 find: (a). (b). (c). (d). ∑( − 3) Solution: (a) = 2 + 1 + 3 + 2 + 3 = 11 (b) = (2)2 + (1)2 + (3)2 + (2)2 + (3)2 = 27 (c) = (2 – 3) + (1 – 3) + (3 – 3) + (2 – 3) + (3 – 3) = –1 –2 + 0 –1 + 0 = – 4
- 3. (d) ∑( − 3) = (2 − 3) + (1 − 3) + (3 − 3) + (2 − 3) + (3 − 3) ∑( − 3) = 1 + 4 + 0 + 1 + 0 = 6 Do yourself (1) A data set contains the observations5, 1, 3, 2, 1 find a. (Ans.12) b. ( Ans.40) c. ( Ans.7) d. ( Ans.21) e. (∑x)2 (Ans.144) (2) If X1 = 11, X2 = 3, X3 = 4, X4 = 5, Evaluate. {Answers: a(13),b(51), c(3.25), d(0), e(8.75)}
- 4. Example-2 Find given that Solution: As shown in given question n = 20 ̅ = ∑ = 226 20 = 11.3 Example-3 Find given that METHOD - I Solution: As shown in given question n = 20 ( − 100) = 226 − (20)(100) = 226 − 2000 = 226 = 226 + 2000 = 2226 = ∑ = 2226 20 = 111.3
- 5. METHOD - II Solution: As shown in given question n = 20 ( − 100) = 226 Let ( − ) = By compairing = 100 = 226 We know that = + ∑ = 100 + = 100 + 11.3 = 111.3