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.

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.

The Mean

The mean is the arithmetic average of the scores.

X_

= iXi

_________

N

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

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.

The Mean

The sum of squared deviations from the Mean is at the lowest value.

X_

Xi -( )2

is lowest

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

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590

580

570

560

550

540

X_

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.