# Week1_pt3 - BEA674 Data and Business Decision Making Week 1...

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BEA674 Data and Business Decision Making Week 1 Numerical Descrip=ve Measures for Univariate and Bivariate Data CIRCOS Provider Code: 00586B

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To describe the proper=es of central tendency, dispersion and shape for univariate numerical data To calculate descrip=ve measures To calculate correla=on between two variables Learning Objec=ves
Numerical Descriptive measures After obtaining raw numerical data, we are typically interested in: Central tendency: a ‘typical’ or ‘representative’ value (e.g. mean, mode, median, geometric mean) Dispersion: amount of ‘spread’ or ‘variation’ in the data (e.g. range, interquartile range, variance, standard deviation, coefficient of variation) Shape (e.g. symmetry, skewness, kurtosis)

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Measuring central tendency Ͳ mean E.g. A statistician is someone who can have his head in an oven and his feet in ice, and says that on the average he feels great . The arithmetic mean (typically referred to as the mean or average ) the most common measure of central tendency. All the values play an equal role in the mean calculation.
Sample mean: Suppose the series Measuring central tendency Ͳ mean (continued) n X X X ,..., , 2 1 the sample mean sample in the values all of summation variable the of ith value size sample or values of number where 1 ... 1 1 2 1 i n i i i n i i n X X X X n X n n X X X X ± ± ± ¦ ¦

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Sample mean: e.g. In a random picked sample, students’ final marks are 80, 55, 72, 64, 60, 88, 92, 18, 78 Measuring central tendency Ͳ mean (continued) 65.56 78) 18 92 88 60 64 72 55 80 ( 9 1 ± ± ± ± ± ± ± ± mean The mean is greatly affected by the extremely low mark 18.
Population mean: Measuring central tendency Ͳ mean (continued) population whole the of size the where 1 1 ¦ N X N N i i X P

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The median is the middle value in an ordered array. If n is an odd number, the median is the middle Ͳ ranked value. If n is an even number, then the median is the average of the two middle ranked value Measuring central tendency Ͳ median array ordered in item ) 2 1 ( median th n ±

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Half of the values are smaller or equal to the median, and half the values are larger than or equal to the median. E.g. In a random picked sample, students’ final marks are 80, 55, 72, 64, 60, 88, 92, 18, 78 Step 1: an ordered array is 18, 55, 60, 64, 72, 78, 80, 88, 92 Step 2: (n+1)/2=(9+1)/2=5. The fifth item is 72. Measuring central tendency Ͳ median(continued)
The median is less sensitive to extreme values. Eg. Instead of having 18 in our last example, we have 50. Then the ordered array becomes 50, 55, 60, 64, 72, 78, 80, 88, 92. The median is the fifth mark 72. Measuring central tendency Ͳ median(continued)

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The mode is the value in a set of data that appears most frequently. Given a set of data, there could be no mode.
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• Spring '14
• Garofalo,LB
• Standard Deviation, Mean, Measuring central tendency, Shape Kurtosis

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