Chapter 3 - Numerical Descriptions of Data.ppt - Numerical Descriptive Measures 1 Chapter Goals After completing this chapter you should be able to \u2022

# Chapter 3 - Numerical Descriptions of Data.ppt - Numerical...

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1 Numerical Descriptive Measures
2 Chapter Goals After completing this chapter, you should be able to: Compute and interpret the mean, median, and mode for a set of data Find the range, variance, and standard deviation and know what these values mean Construct and interpret a box and whiskers plot Compute and explain the coefficient of variation Use numerical measures along with graphs, charts, and tables to describe data
3 Chapter Topics Measures of Center and Location Measures of Variation Measures of Distribution Shape, Relative Location, and Detecting Outliers Exploratory Data Analysis Measures of Association Between Two Variables The Weighted Mean and Grouped Data
4 Summary Measures
5 Notation Conventions Population Parameters are denoted with a letter from the Greek alphabet: µ (mu) represents the population mean (sigma) represents the population standard deviation Sample Statistics are commonly denoted with letters from the Roman alphabet: (X-bar) represents the sample mean s represents the sample standard deviation x
Measures of Center and Location Mean Median Mode Percentiles Quartiles 6
7 Measures of Center and Location
8 Mean (Arithmetic Average) The Mean is the arithmetic average of data values Sample mean Population mean
9 Mean (Arithmetic Average) The most common measure of central tendency Mean = sum of values divided by the number of values Affected by extreme values (outliers)
Seventy efficiency apartments were randomly sampled in a small college town. The monthly rent prices for these apartments are listed in ascending order on the next slide. Sample Mean Example: Apartment Rents
425 430 430 435 435 435 435 435 440 440 440 440 440 445 445 445 445 445 450 450 450 450 450 450 450 460 460 460 465 465 465 470 470 472 475 475 475 480 480 480 480 485 490 490 490 500 500 500 500 510 510 515 525 525 525 535 549 550 570 570 575 575 580 590 600 600 600 600 615 615 Sample Mean i
12 Median In an ordered array, the median is the “middle” number (50% above, 50% below) If n or N is odd, the median is the middle number If n or N is even, the median is the average of the two middle numbers Not affected by extreme values
13 Median To find the median, rank the n values in order of magnitude Find the value in the (n+1)/2 position If n is an even number, let the median be the mean of the two middle-most observations.
Median 425 430 430 435 435 435 435 435 440 440 440 440 440 445 445 445 445 445 450 450 450 450 450 450 450 460 460 460 465 465 465 470 470 472 475 475 475 480 480 480 480 485 490 490 490 500 500 500 500 510 510 515 525 525 525 535 549 550 570 570 575 575 580 590 600 600 600 600 615 615 Averaging the 35th and 36th data values: Median = (475 + 475)/2 = 475
15 Mode A measure of central tendency Value that occurs most often Not affected by extreme values Used for either numerical or categorical data There may be no mode There may be several modes
Mode 425 430 430 435 435 435 435 435 440 440 440 440 440 445 445 445 445 445 450 450 450 450 450 450 450 460 460 460 465 465 465 470 470 472 475 475 475 480 480 480 480 485 490 490 490 500 500 500 500 510 510 515 525 525 525 535 549 550 570 570 575 575 580 590 600 600 600 600 615 615 450 occurred most frequently (7 times) Mode = 450
17 Review Example Five houses on a hill by the beach
18 Summary Statistics Mean: (\$3,000,000/5) = \$600,000 Median: middle value of ranked data = \$300,000 Mode: most frequent value = \$100,000

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