DS212_Chap3_Descriptive_Statistics

# DS212_Chap3_Descriptive_Statistics - C hapte 3 De r...

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1 Chapter 3: Descriptive Statistics – Numerical Measures Sada Soorapanth Spring 2010

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2 Learning Objectives Differentiate between population parameters and sample statistics Distinguish between measures of central tendency and location , measures of variability, measure of relative location Understand the meanings and learn how to compute mean, median, mode percentile, quartile, range, interquartile range (IQR) variance, standard deviation Z-scores Understand the Chebyshev’s theorem and Empirical rule Compute the mean, mode, standard deviation, and variance on grouped data.
3 Population parameters vs Sample statistics x Population Parameters μ , σ 2 μ = population mean σ 2 = population variance = sample average s 2 sample variance x Sample Statistics 2 , s x Collect samples Estimate population parameters 2 , s x 2 , s x

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4 Descriptive statistics: Measure of central tendency Based on 2006 data * , Average prices per gallon are \$3.04 for regular gas (as of Aug. 7) and \$3 for milk. Median age of the US population is 36.2 years. Most popular baby names for boys and girls are Jacob and Emily. The 80 th percentiles of the SAT scores is 1790. *Actual data from the internet
5 Measures of central tendency or location Mean Median Mode Percentiles Quartiles

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6 Mean The mean provides a measure of central location or central tendency of data. Denoted by (for sample) or μ (for population) Data values are denoted by x 1 , x 2 3 ,…. N = number of data in a population, n = number of data in a sample is a point estimator of μ x n x n x x x x x N x N x x x x n i i n N i i N = = = + + + + = = = + + + + = = 1 3 2 1 1 3 2 1 ... average Sample ... mean Population μ x
7 Example: Starting salary of business graduates Monthly salaries for a sample of 12 business school graduates; Graduate Monthly starting Monthly starting salary (\$) 1 2850 7 2890 2 2950 8 3130 3 3050 9 2940 4 2880 10 3325 5 2755 11 2920 6 2710 12

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8 phone usage survey J.D. Powers and Associates surveyed cell phone users in order to learn about the minutes of cell phone usage per month (Associated Press, June 2002). Minutes per month for a sample of 15 cell phone users are shown here; 615430 690 265 180 135830 250 245 380 3951180 420 210 105 What is the mean number of minutes of usage per month?
9 Median The median is the value in the middle when the data are arranged in ascending order (smallest value to largest value). Half of data have values less than or equal to the median (or half have values more or equal to the median). Steps for calculating the median 1. Arrange data in ascending order 2. For an odd number of data, the median is the middle value. For an even number of data, the median is the average of the two middle values. Note: The middle value (s) is located at the (n+1)/2 term.

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10 Example: the median starting salary per month Compute the median starting salary per month for the 12 business college graduates in the previous example.
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DS212_Chap3_Descriptive_Statistics - C hapte 3 De r...

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