Psychology2016

Statistics in Psychology A-5

Figure A.6 A Bimodal Distribution

When a distribution is bimodal, it means that there are two high points instead of just one.

For example, in the pop-quiz scores represented on this graph, there are two “most frequent”

scores—6 and 8. This most likely represents two groups of students, with one group being less

successful than the other.

Some frequency polygons show two high points rather than just one (see Figure A.6)

and are called bimodal distributions. In this example, we have a distribution of scores

from a 10-point pop quiz, and we see that one group of students seemed to do well and

one group didn’t. Bimodal distributions usually indicate that you have two separate

groups being graphed in one polygon. What would the distribution of height for men and

women look like?

MEASURES OF CENTRAL TENDENCY

A.3 Identify three measures of central tendency and explain how they are

impacted by the shape of the distribution.

A frequency distribution is a good way to look at a set of numbers, but there’s still a

lot to look at—isn’t there some way to sum it all up? One way to sum up numerical

data is to find out what a “typical” score might be, or some central number around

which all the others seem to fall. This kind of summation is called a measure of central

tendency, or the number that best represents the central part of a frequency distribu-

tion. There are three different measures of central tendency: the mean, the median,

and the mode.

MEAN The most commonly used measure of central tendency is the mean, the arith-

metic average of a distribution of numbers. That simply indicates that you add up all

the numbers in a particular set and then divide them by how many numbers there are.

This is usually the way teachers get the grade point average for a particular student,

for example. If Rochelle’s grades on the tests she has taken so far are 86, 92, 87, and 90,

then the teacher would add 86 + 92 + 87 + 90 = 355, and then divide 355 by 4 (the num-

ber of scores) to get the mean, or grade point average, of 88.75. Here is the formula for

the mean:

Mean = SX#N

bimodal distributions

frequency distribution in which there

are two high points rather than one.

measure of central tendency

numbers that best represent the

most typical score of a frequency

distribution.

mean

the arithmetic average of a

distribution of numbers.

Figure A.5 Skewed Distribution

These frequency polygons show how distribu-

tions can be skewed in two different directions.

The graph on the left represents the frequency

of heights among Hobbits (the little people from

the fantasy The Lord of the Rings) and is pos-

itively skewed because the long “tail” goes to

the right, or positive direction. The graph on the

right shows the frequency of heights among NBA

basketball players and is negatively skewed—the

tail points to the left.

Fr

equency

Height of hobbits Height of NBA

players

Positive

skew

Negative

skew

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