Quantitative Problem Solving Notes-Lecture one

Quantitative Problem Solving Notes-Lecture one - Lamb...

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= 2 Lamb Lecture1 Fall 2009 MBA612 4 Rules of Summation X i 5X i 1) 20 100 2) 18 90 3) 22 110 4) 25 125 5) 15 75 500 = i 15X i = 100 5X i = 500, The above approach uses case by case method. That is, for each value of I, the value of 5x i is found and then these values are summed. Rule #1 = i 1nK X i = = Ki 1nX i 500 = 5(100) = 500 Here the expression is simplified by pulling the constant out of the expression. Rule #2 (X i + Y i ) (X i + Y i ) = X i + Y i A summation expression can be broken down into its parts Likewise (X i - Y i ) = X i - Y i X i Y i X i + Y i 1) 20 2 22 2) 18 1 19 3) 22 0 22 4) 25 2 27 5) 15 1 16 100 6 106 Here, again, we have found the value of the expression case by case then summed.
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Lamb Lecture1 Fall 2009 MBA612 Also, (X i + Y i ) = X i + Y i = 100 + 6 = 106 Here we have simplified the expression and found the same answer. Rule #3 The sum of a constant n times is = = i 1nK nk Rule #4 = i 1nX i Y i X i Y i X i Y i 1) 20 2 40 2) 18 1 18 3) 22 0 0 4) 25 2 50 5) 15 1 15 100 6 123 = X 1 Y 1 + X 2 Y 2 + … X 5 Y 5 = i 1nX i Y i ( X ≠ ∑ i ) ( Y i ) 123 100 x 6 That is, one cannot find the value of the quantity on the left hand side of the expression by using the expression on the right hand side and visa versa. The following is a formula for sample variance. As one moves from the first formula to the second formula, one uses all the rules of summation. S 2 = (X i X ) 2 (n-1) S 2 = n X i – ( X i ) 2 n (n – 1) Statistics X is the sample mean X = X i n This is used for sample data.
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Lamb Lecture1 Fall 2009 MBA612 Property of this Statistic E ( X ) = μ , This means, the expected value of the sample mean is the population mean. Parameter Definition of Parameter — μ is the average value of all X This formula is used when you have all the data and not a sample of data. μ = = i 1NxiN μ = E (X) μ is again defined as the population average value of x. σX = / σ n The standard error of the mean μ Central Limit Theorem—Sample means are normally distributed about the population mean. The standard deviation of sample means is called the standard error. Note the picture above. Double Summation Notation An example, Calculate = = j 1ri 1nXij using the following data i/j 1 2 1) 20 30 2) 22 32 3) 18 28 4) 25 35 5) 15 25 100 150 = = j 12i 15Xij = = i 15X i1 + = i 15X i2 (X 11 + X 21 + X 31 + X 41 + X 51 ) + (X 12 + X 22 + X 32 + X 42 + X 52 ) 20 + 22 + 18+ 25 + 15 + 30 + 32 + 28 + 35 + 25 100 + 150 =250 Measures of Central Tendency
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Lamb Lecture1 Fall 2009 MBA612 Mean X = X/n Mode value that occurs most frequently Median value that is in the middle once you arrange them in order Median, arrange the data in order from smallest to largest 5 8 12 average of these two 16
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This note was uploaded on 08/24/2010 for the course MATH 267 taught by Professor Chandrasekhar during the Summer '10 term at Anna University Chennai - Regional Office, Coimbatore.

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Quantitative Problem Solving Notes-Lecture one - Lamb...

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