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Statistics for the Behavioral Sciences, 4/e

Michael Thorne, Mississippi State University -- Mississippi State
Martin Giesen, Mississippi State University -- Mississippi State

Measures of Central Tendency

Problems

For the following distributions, try to give the three measures of central tendency without computing them. After you have done this, compute <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif:: ::/sites/dl/free/0072832517/55314/c5_s1.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (0.0K)</a> for each distribution.
1. 6, 10, 10, 14
2. 7, 8, 9
3. 1, 2, 3, 3, 4, 5
4. X f
  20 1
  18 2
  16 4
  14 2
  12 1
Using the following distribution, find each of the three measures of central tendency. Show that the mean is the balancing point in the distribution—that is, .
X f
10 1
9 2
8 1
7 4
6 6
5 5
4 2
3 1
2 1
A neuroticism scale consisting of 10 items has been given to 50 individuals; higher scores mean greater neuroticism. The frequency distribution of their scores is as follows:
X f
10 4
9 4
8 5
7 7
6 8
5 7
4 5
3 4
2 4
1 2
Find the mean, median, and mode of the scores.
A recall test of retention has been given after 25 students have studied briefly a list of 15 nouns. Determine the mean, median, and mode of the results.
X f
6 2
5 0
4 6
3 5
2 8
1 3
0 1
The following data were obtained for 25 students given a recognition test of retention of 15 previously studied nouns. Find the median, mode, and mean.
X f
15 7
14 6
13 4
12 2
10 3
8 1
6 2
ACT scores have been determined for 26 students in an honors introductory psychology class and are shown in the following frequency distribution. Compute the mean, the median, and the mode.
X f
33 1
31 1
30 3
29 4
28 4
27 8
26 2
25 2
24 1
N = 26
In a study of 15 rats, the latency to enter a darkened chamber has been recorded. If the animal didn't enter within 60 seconds, the trial was terminated and the animal received a score of 60. Determine the most appropriate measure of central tendency.
X f
60 2
45 2
43 1
42 1
35 2
33 3
32 1
25 1
20 1
10 1
Omitting the nonresponders, determine all three measures of central tendency.
Using the rules for rounding, round each of the following. For each of your answers, cite the applicable rule.
1. 1.4549 to hundredths
2. 1.5551 to hundredths
3. 3.66666 to hundredths
4. 23.33333 to hundredths
5. 7.825137 to hundredths

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