Psychology2016

Statistics in Psychology A-7

MODE The mode is another measure of central tendency,

in which the most frequent score is taken as the central

measure. In the numbers given in Table A.2, the mode

would be 100 because that number appears more times

in the distribution than any other. Three people have that

score. This is the simplest measure of central tendency

and is also more useful than the mean in some cases,

especially when there are two sets of frequently appear-

ing scores. For example, suppose a teacher notices that on

the last exam the scores fall into two groups, with about

15  students making a 95 and another 14 students making a

67. The mean and the median would probably give a num-
    ber somewhere between those two scores—such as 80.
    That number tells the teacher a lot less about the distribu-
    tion of scores than the mode would because, in this case,
    the distribution is bimodal—there are two very different
    yet very frequent scores. (Refer to Figure A.6 for another
    example.)

MEASURES OF CENTRAL TENDENCY AND THE SHAPE

OF THE DISTRIBUTION When the distribution is normal

or close to it, the mean, median, and mode are the same

or very similar. There is no problem. When the distribu-

tion is not normal, then the situation requires a little more

explanation.

SKEWED DISTRIBUTIONS If the distribution is skewed, then the mean is pulled in the

direction of the tail of the distribution. The mode is still the highest point, and the median

is between the two. Let’s look at an example. In Figure A.7 we have a distribution of

salaries at a company. A few people make a low wage, most make a mid-level wage, and

the bosses make a lot of money. This gives us a positively skewed distribution with the

measures of central tendency placed as in the figure. As mentioned earlier, with such a

distribution, the median would be the best measure of central tendency to report. If the

distribution were negatively skewed (tail to the left), the order of the measures of central

tendency would be reversed.

BIMODAL DISTRIBUTIONS If you have a bimodal distribution, then none of the measures

of central tendency will do you much good. You need to discover why you appear to

have two groups in your one distribution.

MEASURES OF VARIABILITY

A.4 Identify the types of statistics used to examine variations in data.

Descriptive statistics can also determine how much the scores in a distribution differ,

or vary, from the central tendency of the data. These measures of variability are used

to discover how “spread out” the scores are from each other. The more the scores

cluster around the central scores, the smaller the measure of variability will be, and

the more widely the scores differ from the central scores, the larger this measurement

will be.

There are two ways that variability is measured. The simpler method is by calculat-

ing the range of the set of scores, or the difference between the highest score and the low-

est score in the set of scores. The range is somewhat limited as a measure of variability

Figure A.7 Positively Skewed Distribution

In a skewed distribution, the high scores on one end will cause the mean to be

pulled toward the tail of the distribution, making it a poor measure of central

tendency for this kind of distribution. For example, in this graph, many workers

make very little money (represented by the mode), while only a few workers

make a lot of money (the tail). The mean in this case would be much higher

than the mode because of those few high scores distorting the average. In this

case, the median is a much better measure of central tendency because it tends

to be unaffected by extremely high or extremely low scores such as those in

this distribution.

Poorly

paid

workers

Typical workers

Highly paid bosses

Median

Mode Mean

mode

the most frequent score in a

distribution of scores.

measures of variability

measurement of the degree

of  differences within a distriDution or

how the scores are spread out.

range

the difference between the highest

and lowest scores in a distribution.

bimodal

condition in which a distribution has

two modes.

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