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# MEASURES OF CENTRAL TENDENCY

Fill
in the blanks:

4.1. The
score that repeats the most often in a distribution is called the ______.

4.2. The
descriptive statistic used the most in inferential statistics as a measure of
central tendency is the _________.

4.3. The
measure of central tendency used with nominal scale data is the _______.

4.4. To
find the mean of a sample, thethe sum of the scoresas is divided by ______.

4.5.In
a positively skewed distribution, the majority of the scores cluster above/below
the ________.

4.6.The
mode and the mean have the same values in distributions that are normal/negatively
skewed
.

4.7.Distributions
with few scores are more/less likely to have a mode than distributions
with many scores.

the following questions:

4.8.Which
measure of central tendency would be the most appropriate for summarizing the
following test scores? Explain your choice.

13, 14, 10, 38, 11, 12, 16, 15

4.9.What
is the difference between
andm?
How are they related to each other?

4.10. A
distribution of 10 scores has a mean of 6. Following are 9 scores of this distribution. Which score is missing (remember that the
mean should be 6)?

4, 8, 10, 5, 9, 3, 6, 7, 3

4.11.
When the sum of a group
of scores is 280 and the mean of the scores is 7, how many scores are in the
distribution?

4.12. Find
the mode, median, and mean of the distribution depicted in the following
histogram:

Frequency

 Scores

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MEASURES OF VARIABILITY

Circle

5.1. The
distance between the highest and the lowest scores is called the range/variance.

5.2. The
SD is equal to the square root of the mean/variance.

5.3.A
test with 30 items is likely to have a higher/lower standard deviation
that a test with 80 items.

5.4.The
mean of the squared deviation scores is called the variance/standard deviation.

5.5.The
SD of the number of errors found by an auditor in a sample of accounts of one
company is likely to be higher/lower
than the SD of the number of errors found in samples taken from a number of
different companies.

5.6. The
SD is/is not sensitive to
extreme scores.

5.7. The
variance of the population is represented by S2/s2.

5.8.
In most cases, the variance is larger/smaller
than the SD.

5.9.The
measure of variability that takes into consideration every score in the
distribution is the range/standard deviation.

the following questions:

5.10. Study
the following three distributions. What are the similarities and differences
between the three distributions in terms of their means, ranges, and standard
deviations? (Note: Assume the three distributions to be samples if you decide
to compute their standard deviations.)

Distribution A: 8, 9, 6, 12, 5

Distribution B: 7, 10, 11, 8, 4

Distribution C: 7, 9, 8, 9, 7

5.11. Three
statistics classes (Sections A, B and C), each with 26 students, took the same
test. The SD of Section A was 7; the SD of Section B was 16; and the SD of
Section C was 10. Which class was more homogeneous in regard to the
scores on the test?

5.12. Means
and standard deviations were calculated for an Overall Quality Assurance Test
with 45 items. This test consists of 20 Input Factors and 25 Output
Factors. Estimate which of the
following standard deviations was obtained for the total Quality Assurance Test
and which standard deviation was obtained for the Input factors.

a. SD = 5.7 b. SD = 8.3

5.13. Shortly
after being hired, eight sales trainees participated in a role playing exercise
where they were rated on a scale of 1-10 on their ability to close a sale.
After one week of training, the same eight sales trainees participated in the
same role playing exercise and their closing skills were evaluated using the
same scale of 1-10.

Review the following scores. Is there a
difference between the pre-training and post-training rating scores? What effect,
if any, did the training have on the trainees? Explain.

 Trainee Pre-training Post-training A 9.5 9.1 B 7.8 8.9 C 9.9 9.1 D 8.6 8.8 E 8.2 8.8 F 9.6 9.0 G 8.6 8.9 H 9.1 9.0 Mean 8.91 8.95 SD 0.73 0.12

5.14. Following
is a graph showing two distributions weekly incomes of employees working in the
same industry. The means and standard deviations of the two groups are also
given. Estimate which of the two means and which of the two SDs belong to each
group of students.

Mean
= \$530 SD = \$70

Mean
= \$690 SD = \$150

.0/msohtmlclip1/01/clip_image003.png”>

A B

Group A: The mean is ______ and the SD
is _______

Group B: The mean is ______ and the SD
is_______

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