商务与经济统计ppt第3章A
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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
Slide 10
Median
For an even number of observations: 26 18 27 12 14 27 30 19 8 observations 12 14 18 19 26 27 27 30 in ascending order
the median is the average of the middle two values. Median = (19 + 26)/2 = 22.5
Median = 19
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 11
Median
Example: Apartment Rents Averaging the 35th and 36th data values: Median = (475 + 475)/2 = 475
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
values. The sample mean x is the point estimator of the
population mean m.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 1
Chapter 3, Part A Descriptive Statistics: Numerical Measures
Measures of Location Measures of Variability
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Statistics for Business and Economics
Anderson Sweeney Williams
Slides by
John Loucks
St. Edward’s University
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 5
Population Mean m
xi
m
N
Sum of the values of the N observations
Number of observations in the population
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
445 615 430 590 435 600 460 600 440 615 440 440 440 525 425 445 575 445 450 450 465 450 525 450 450 460 435 460 465 480 450 470 490 472 475 475 500 480 570 465 600 485 580 470 490 500 549 500 500 480 570 515 450 445 525 535 475 550 480 510 510 575 490 435 600 435 445 435 430 440
corresponding population parameter.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 3
Mean
Perhaps the most important measure of location is the mean.
The mean provides a measure of central location. The mean of a data set is the average of all the data
Slide 6
Biblioteka Baidu
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 below.
Slide 4
Sample Mean x
xi
x n
Sum of the values of the n observations
Number of observations in the sample
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 12
Trimmed Mean
Another measure, sometimes used when extreme values are present, is the trimmed mean.
It is obtained by deleting a percentage of the smallest and largest values from a data set and then computing the mean of the remaining values.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Note: Data is in ascending order.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 9
Median
For an odd number of observations: 26 18 27 12 14 27 19 7 observations
12 14 18 19 26 27 27 in ascending order the median is the middle value.
Slide 2
Measures of Location
Mean Median Mode Percentiles Quartiles
If the measures are computed for data from a sample,
they are called sample statistics.
Slide 8
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.
Slide 7
Sample Mean
Example: Apartment Rents
x xi 34, 356 490.80 n 70
445 615 430 590 435 600 460 600 440 615 440 440 440 525 425 445 575 445 450 450 465 450 525 450 450 460 435 460 465 480 450 470 490 472 475 475 500 480 570 465 600 485 580 470 490 500 549 500 500 480 570 515 450 445 525 535 475 550 480 510 510 575 490 435 600 435 445 435 430 440
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
they are called population parameters.
A sample statistic is referred to as the point estimator of the
Slide 10
Median
For an even number of observations: 26 18 27 12 14 27 30 19 8 observations 12 14 18 19 26 27 27 30 in ascending order
the median is the average of the middle two values. Median = (19 + 26)/2 = 22.5
Median = 19
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 11
Median
Example: Apartment Rents Averaging the 35th and 36th data values: Median = (475 + 475)/2 = 475
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
values. The sample mean x is the point estimator of the
population mean m.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 1
Chapter 3, Part A Descriptive Statistics: Numerical Measures
Measures of Location Measures of Variability
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Statistics for Business and Economics
Anderson Sweeney Williams
Slides by
John Loucks
St. Edward’s University
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 5
Population Mean m
xi
m
N
Sum of the values of the N observations
Number of observations in the population
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
445 615 430 590 435 600 460 600 440 615 440 440 440 525 425 445 575 445 450 450 465 450 525 450 450 460 435 460 465 480 450 470 490 472 475 475 500 480 570 465 600 485 580 470 490 500 549 500 500 480 570 515 450 445 525 535 475 550 480 510 510 575 490 435 600 435 445 435 430 440
corresponding population parameter.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 3
Mean
Perhaps the most important measure of location is the mean.
The mean provides a measure of central location. The mean of a data set is the average of all the data
Slide 6
Biblioteka Baidu
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 below.
Slide 4
Sample Mean x
xi
x n
Sum of the values of the n observations
Number of observations in the sample
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 12
Trimmed Mean
Another measure, sometimes used when extreme values are present, is the trimmed mean.
It is obtained by deleting a percentage of the smallest and largest values from a data set and then computing the mean of the remaining values.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Note: Data is in ascending order.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 9
Median
For an odd number of observations: 26 18 27 12 14 27 19 7 observations
12 14 18 19 26 27 27 in ascending order the median is the middle value.
Slide 2
Measures of Location
Mean Median Mode Percentiles Quartiles
If the measures are computed for data from a sample,
they are called sample statistics.
Slide 8
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.
Slide 7
Sample Mean
Example: Apartment Rents
x xi 34, 356 490.80 n 70
445 615 430 590 435 600 460 600 440 615 440 440 440 525 425 445 575 445 450 450 465 450 525 450 450 460 435 460 465 480 450 470 490 472 475 475 500 480 570 465 600 485 580 470 490 500 549 500 500 480 570 515 450 445 525 535 475 550 480 510 510 575 490 435 600 435 445 435 430 440
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.