wednesday, september 30
DESCRIPTION
Wednesday, September 30. Central Tendency of Distributions (Mean, Median, Mode). The mode . The mode is the score with the highest frequency of occurrences. It is the easiest score to spot in a distribution. It is the only way to express the central tendency of a nominal level variable. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Wednesday, September 30](https://reader035.vdocuments.us/reader035/viewer/2022062309/56813b9d550346895da4d3ac/html5/thumbnails/1.jpg)
Wednesday, September 30
Central Tendency of Distributions
(Mean, Median, Mode)
![Page 2: Wednesday, September 30](https://reader035.vdocuments.us/reader035/viewer/2022062309/56813b9d550346895da4d3ac/html5/thumbnails/2.jpg)
The mode.
The mode is the score with the highest frequency of occurrences.
It is the easiest score to spot in a distribution.
It is the only way to express the central tendency of a nominal level variable.
![Page 3: Wednesday, September 30](https://reader035.vdocuments.us/reader035/viewer/2022062309/56813b9d550346895da4d3ac/html5/thumbnails/3.jpg)
The median.
The median is the middle-ranked score (50th percentile).
If there is an even number of scores, it is the arithmetic average of the two middle scores.
The median is unchanged by outliers. Even if Bill Gateswere deleted from the U.S. economy, the median asset of U.S. citizens would remain (more or less) the same.
![Page 4: Wednesday, September 30](https://reader035.vdocuments.us/reader035/viewer/2022062309/56813b9d550346895da4d3ac/html5/thumbnails/4.jpg)
The Mean
The mean is the arithmetic average of the scores.
X_
= iXi
_________
N
![Page 5: Wednesday, September 30](https://reader035.vdocuments.us/reader035/viewer/2022062309/56813b9d550346895da4d3ac/html5/thumbnails/5.jpg)
The Mean
The mean is the arithmetic average of the scores.
The mean is the center of gravity of a distribution. DeletingBill Gates’ assets would change the national mean income.
X_
= iXi
_________
N
![Page 6: Wednesday, September 30](https://reader035.vdocuments.us/reader035/viewer/2022062309/56813b9d550346895da4d3ac/html5/thumbnails/6.jpg)
The mean of a group of scores is that point on the number linesuch that the sum of the squared distances of all scores to that pointis smaller than the sum of the squared distances to any other point.
![Page 7: Wednesday, September 30](https://reader035.vdocuments.us/reader035/viewer/2022062309/56813b9d550346895da4d3ac/html5/thumbnails/7.jpg)
The Mean
The sum of squared deviations from the Mean is at the lowest value.
X_
Xi -( )2
is lowest
![Page 8: Wednesday, September 30](https://reader035.vdocuments.us/reader035/viewer/2022062309/56813b9d550346895da4d3ac/html5/thumbnails/8.jpg)
The Mean
The sum of squared deviations from the Mean is at the lowest value.
X_
Xi -( )2
is lowest
T
1.61.41.21.0.8.6.4
DIS
2
610
600
590
580
570
560
550
540
X_
![Page 9: Wednesday, September 30](https://reader035.vdocuments.us/reader035/viewer/2022062309/56813b9d550346895da4d3ac/html5/thumbnails/9.jpg)
The Mean
The mean is the arithmetic average of the scores.
The mean is the center of gravity of a distribution. DeletingBill Gates’ assets would change the national mean!
The sum of squared deviations from the Mean is at the lowest value.
The mean is not a good measure of central tendency if thereare outliers.
![Page 10: Wednesday, September 30](https://reader035.vdocuments.us/reader035/viewer/2022062309/56813b9d550346895da4d3ac/html5/thumbnails/10.jpg)
![Page 11: Wednesday, September 30](https://reader035.vdocuments.us/reader035/viewer/2022062309/56813b9d550346895da4d3ac/html5/thumbnails/11.jpg)