Lectures Applied statistics for business: Chapter 3 - ThS. Nguyễn Tiến Dũng

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Lectures "Applied statistics for business - Chapter 3: Numerical measures" provides students with the knowledge: Measures of location, measures of variability, measures of distribution shape, relative location, and detection of outliers. Invite you to refer to the disclosures.

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Nội dung Text: Lectures Applied statistics for business: Chapter 3 - ThS. Nguyễn Tiến Dũng

Chapter 3 NUMERICAL MEASURES MBA Nguyen Tien Dung School of Economics and Management Website: https://sites.google.com/site/nguyentiendungbkhn Email: dung.nguyentien3@hust.edu.vn
Main Contents 3.1 MEASURES OF LOCATION 3.2 MEASURES OF VARIABILITY 3.3 MEASURES OF DISTRIBUTION SHAPE, RELATIVE LOCATION, AND DETECTION OF OUTLIERS © Nguyễn Tiến Dũng Applied Statistics for Business 2
3.1 MEASURES OF LOCATION ● Mean ● Median ● Mode ● Percentiles ● Quartiles © Nguyễn Tiến Dũng Applied Statistics for Business 3
Mean ● A population, say, a data set about Population mean the ages of students in 5 classes. We denote: N 1 ● X: the random variable of age ● X1, X2, …, XN  N X i 1 i ● N – population size (say N = 200) ● A random sample taken from a population Sample mean ● x1, x2, …, xn 1 n ● n – sample size (say, n = 30) x   xi ● The sample mean is the unbiased n i 1 point estimator of the population mean © Nguyễn Tiến Dũng Applied Statistics for Business 4
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Median ● The median is the value in the middle when the data are arranged in ascending order (smallest value to largest value). ● A set of observations: x1, x2, …, xn ● Arrange the data in ascending order (smallest value to largest value). ● Me = x(n+1)/2 ● If n = 2k+1, then Me = xk+1 ● If n = 2k, then Me = 0.5(xk + xk+1) ● Sample 1: 1 3 5 8 10 n = 5  k = 2  k+1 = 3 ● Sample 2: 1 3 5 8 9 10  (n+1)/2 = 3.5 © Nguyễn Tiến Dũng Applied Statistics for Business 9
Mode ● The mode is the value that occurs with greatest frequency. ● 1 1 2 2 3 4 4 4 5 5 6 6  Mode = 4 ● 1 2 2 3 4 4 4 5 5 6 6 6  Mode = 4, 6 (multiple modes) ● 1 1 2 2 3 3 4 4 5 5 6 6  no Mode © Nguyễn Tiến Dũng Applied Statistics for Business 10
Percentile (Textbook) ● Anderson 2014: The pth percentile is a value such that at least p percent of the observations are less than or equal to this value and at least (100 - p) percent of the observations are greater than or equal to this value. © Nguyễn Tiến Dũng Applied Statistics for Business 11
Percentile (Excel) ● Position of the kth percentile: ● pk = k.(n-1)/100 + 1 ● Value of the pth percentile: ● if pk is integer -> x(pk) ● if pk is not an integer, use the interpolation procedure © Nguyễn Tiến Dũng Applied Statistics for Business 12
Quartiles ● Q1: the first quartile = the 25th percentile ● Q2: the second quartile = the 50th percentile = Median ● Q3: the third quartile = the 75th percentile © Nguyễn Tiến Dũng Applied Statistics for Business 13
Quartiles (Excel & MegaStat) ● Q1: The first quartile ● Position: q1 = [1*(n-1)/4] +1 ● Value: Q1 = x(q1) ● Q2 ● Position: q2 = [2*(n-1)/4] +1 ● Value: Q2 = x(q2) = Median ● Q3 ● Position: q3 = [3*(n-1)/4] +1 ● Value: Q3 = x(q3) ● Recommend: Use Excel & MegaStat procedure © Nguyễn Tiến Dũng Applied Statistics for Business 14
3.2 MEASURES OF VARIABILITY ● Range ● Interquartile Range ● Variance ● Standard Deviation ● Coefficient of Variation © Nguyễn Tiến Dũng Applied Statistics for Business 15
Different Variances © Nguyễn Tiến Dũng Applied Statistics for Business 16
● Range = Max - Min ● Interquartile Range = Q3 – Q1 ● Population Variance 2 and Population Standard Deviation  N N  (X i  ) 2  i ( X   ) 2 2  i 1   2  i 1 N N ● Sample Variance s2 & Sample Standard Deviation s n n  ( xi  x ) 2  i ( x  x ) 2 s2  i 1 s  s2  i 1 n 1 n 1 © Nguyễn Tiến Dũng Applied Statistics for Business 17
Calculating the Mean and Std. Deviation ● Sample Data ● Sample Variance = 256 / 4 = 64 ● Sample Std. Deviation = sqrt(64) = 8 © Nguyễn Tiến Dũng Applied Statistics for Business 18
Sample Variance & Standard Deviation © Nguyễn Tiến Dũng Applied Statistics for Business 19
Coefficient of Variation ● A measure of how large the standard deviation is relative to the mean, expressed as a percentage.  s CV   100% or CV   100%  x © Nguyễn Tiến Dũng Applied Statistics for Business 20