Psychology2016

A-6 APPENDIX A

What does this mean?

• S is a symbol called sigma. It is a Greek letter and it is also called the summation sign.


• X represents a score. Rochelle’s grades are represented by X.


• SX means add up or sum all the X scores or SX = 86 + 92 + 37 + 90 = 355.


• N means the number of scores. In this case, there are four grades.


• We then divide the sum of the scores (SX) by N to get the mean or

Mean = SX#N =

355

4 = 88.75

The mean is a good way to find a central tendency if the set of scores clusters

around the mean with no extremely different scores that are either far higher or far lower

than the mean.

You may hear or read about a concept called “regression to the mean.” This is a

concept that describes the tendency for measurements of a variable to even out over the

course of the measurements (Stigler, 1997). If a measurement is fairly high at first, sub-

sequent measurements will tend to be closer to the mean, the average measurement, for

example. This is one of the reasons that researchers want to replicate measurements many

times rather than relying on the first results, which could cause them to draw incorrect

conclusions from the data.

MEDIAN

I remember that sometimes my teacher would “curve” the grades

for a test, and it was always bad when just one person did really

well and everyone else did lousy—is that what you mean about

extremely different scores?

Yes, the mean doesn’t work as well when there are extreme scores, as you would

have if only two students out of an entire class had a perfect score of 100 and everyone

else scored in the 70s or lower. If you want a truer measure of central tendency in such a

case, you need one that isn’t affected by extreme scores. The median is just such a mea-

sure. A median is the score that falls in the middle of an ordered distribution of scores.

Half of the scores will fall above the median, and half of the scores will fall below it. If

the distribution contains an odd number of scores, it’s just the middle number, but if the

number of scores is even, it’s the average of the two middle scores. The median is also the

50th percentile. Look at Table A.2 for an example of the median.

The mean IQ of this group would be 114.6, but the median would be 101 (the aver-

age between Evan with 102 and Fethia with 100, the average of the two middle numbers).

This may not look like much of a difference, but it’s really a change of about 13.6 IQ

points—a big difference. Also, think about measures of income in a particular area. If

most people earn around $35,000 per year in a particular area, but there are just a few

extremely wealthy people in the same area who earn $1,000,000 a year, a mean of all the

annual incomes would no doubt make the area look like it was doing much better than

it really is economically. The median would be a more accurate measure of the central

tendency of such data.

median

the middle score in an ordered

distribution of scores, or the mean

of the two middle numbers; the

th Rercentile.

Table A.2 Intelligence Test Scores For 10 People

Name Allison Ben Carol Denise Evan Fethia George Hal Inga Jay

IQ^1601501391021021001001009895

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