Psychology2016

A-4 APPENDIX A

Figure A.3 The Normal Curve

The normal curve, also known as the bell curve

because of its unique shape, is often the way in

which certain characteristics such as intelligence

or weight are represented in the population. The

highest point on the curve typically represents the

average score in any distribution.

off below four glasses and above eight glasses a day (variability). Our frequency poly-

gon has a high point, and the frequency decreases on both sides.

A common frequency distribution of this type is called the normal curve. It has a

very specific shape and is sometimes called the bell curve. Look at Figure A.3. This curve

is almost a perfect normal curve, and many things in life are not that perfect. The normal

curve is used as a model for many things that are measured, such as intelligence, height,

or weight, but even those measures only come close to a perfect distribution (provided

large numbers of people are measured). One of the reasons that the normal curve is so

useful is that it has very specific relationships to measures of central tendency and a mea-

surement of variability, known as the standard deviation.

OTHER DISTRIBUTION TYPES: SKEWED AND BIMODAL Distributions aren’t always

normal in shape. Some distributions are described as skewed. This occurs when the dis-

tribution is not even on both sides of a central score with the highest frequency (like

in our example). Instead, the scores are concentrated toward one side of the distribu-

tion. For example, what if a study of people’s water-drinking habits in a different class

revealed that most people drank around seven to eight glasses of water daily, with no

one drinking more than eight? The frequency polygon shown in Figure A.4 reflects this

very different distribution.

In this case, scores are piled up in the high end, with most people drinking seven

or eight glasses of water a day. The graphs in Figure A.5 show a skewed distribution.

Skewed distributions are called positively or negatively skewed, depending on where

the scores are concentrated. A concentration in the high end would be called negatively

skewed. A concentration in the low end would be called positively skewed. The direc-

tion of the extended tail determines whether it is positively (tail to right) or negatively

(tail to left) skewed. Here’s an example. What do you think about the distribution of

heights of Hobbits (the little guys from The Lord of the Rings) and NBA basketball players

(who are usually tall)? Might not these frequency distributions of height in Figure A.5 be

appropriate?

negatively skewed

a distribution of scores in which scores

are concentrated in the high end

of the distriDution.

positively skewed

a distribution of scores in which scores

are concentrated in the low end of the

distribution.

skewed distribution

frequency distribution in which most

of the scores fall to one side or the

other of the distribution.

Figure A.4 A Frequency Polygon

Skewed distributions are those in which the most frequent scores occur at one end or the other of the distribution, as represented by this frequency

polygon, in which most people are seen to drink at least seven to eight glasses of water each day.

Interactive

Number of students

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40 50 60 70

Grades on midterm exam

80 90100

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