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Chapter3 - Elementary Statistics Workshop Chapter3...

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Elementary Statistics Workshop Chapter3. Descriptive Statistics: Numerical Measures
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Part A: 1. Measures of Location 2. Measures of Variability
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If the measures are computed for data from a sample, they are called sample statistics . If the measures are computed for data from a population, they are called population parameters . A sample statistic is referred to as the point estimator of the corresponding population parameter. Mean Measure of Location Median Mode Percentiles Quartiles
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The mean of a data set is the average of all the data values. The sample mean is the point estimator of the population mean m . x Mean
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Population Mean m Number of observations in the population Sum of the values of the N observations i x N m
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Sample Mean Example: Apartment Rents Seventy efficiency apartments were randomly sampled in a small college town. The monthly rent prices for these apartments are listed in ascending order as below 425 430 435 440 445 450 460 465 470 472 475 480 485 490 500 510 515 525 535 549 550 570 575 580 590 600 615
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34,356 490.80 70 i x x n    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
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Median The median of a data set is the value in the middle when the data items are arranged in ascending order. Whenever a data set has extreme values, the median is the preferred measure of central location. The median is the measure of location most often reported for annual income and property value data. A few extremely large incomes or property values can inflate the mean.
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12 14 19 26 27 18 27 For an odd number of observations: in ascending order 26 18 27 12 14 27 19 7 observations the median is the middle value. Median = 19 Median
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12 14 19 26 27 18 27 For an even number of observations: in ascending order 26 18 27 12 14 27 30 8 observations the median is the average of the middle two values. Median = (19 + 26)/2 = 22.5 19 30 Median
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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 Median
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Mode The mode of a data set is the value that occurs with greatest frequency. The greatest frequency can occur at two or more different values. If the data have exactly two modes, the data are bimodal. If the data have more than two modes, the data are multimodal.
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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 Mode
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Percentiles A percentile provides information about how the data are spread over the interval from the smallest value to the largest value.
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Chapter3 - Elementary Statistics Workshop Chapter3...

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