Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

76 CHAPTER 3 | Central Tendency
FIGURE 3.4
A distribution of N 5 5 scores that is
balanced at the mean, μ 5 7.
1 2 3 546 7 8 9 10 11 12 13
score or removing an existing score will cause the mean to change unless the new score (or
existing score) is located exactly at the mean.
The following example demonstrates exactly how the new mean is computed when a
new score is added to an existing sample.
EXAMPLE 3.5
Adding a score (or removing a score) has the same effect on the mean whether the original
set of scores is a sample or a population. To demonstrate the calculation of the new mean,
we will use the set of scores that is shown in Figure 3.4. This time, however, we will treat
the scores as a sample with n = 5 and M = 7. Note that this sample must have SX = 35.
What will happen to the mean if a new score of X = 13 is added to the sample?
To find the new sample mean, we must determine how the values for n and SX will be
changed by a new score. We begin with the original sample and then consider the effect of
adding the new score. The original sample had n = 5 scores, so adding one new score will
produce n 5 6. Similarly, the original sample had SX = 35. Adding a score of X = 13 will
increase the sum by 13 points, producing a new sum of SX = 35 + 13 = 48. Finally, the
new mean is computed using the new values for n and SX.
M 5 SX
n 5 48 6 5 8
The entire process can be summarized as follows:
Original
Sample
New Sample,
Adding X 5 13
n 5 5 n 5 6
SX 5 35 SX 5 48
M 5 35
5 5 7 M 5 48
6 5 8
The following example is an opportunity for you to test your understanding by determining
how the mean is changed by removing a score from a distribution.
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EXAMPLE 3.6
We begin with a sample of n = 5 scores with SX = 35 and M = 7. If one score with a value
of X = 11 is removed from the sample, what is the mean for the remaining scores? You
should obtain a mean of M = 6. Good luck and remember that you can use Example 3.5 as
a model.
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Adding or Subtracting a Constant from Each Score If a constant value is added to
every score in a distribution, the same constant will be added to the mean. Similarly, if you
subtract a constant from every score, the same constant will be subtracted from the mean.
In the Preview for this Chapter (page 68), we described a study that examined the effect
of alcohol consumption on the perceived attractiveness of opposite-sex individuals shown
in photographs (Jones et al., 2003). The results showed that alcohol significantly increased
ratings of attractiveness.