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# Central Tendency and Comparing Measures Variability

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Problem: Chapter 3, problems 6, 14, 16, 22, 24, 26; Chapter 4, problems
2, 4, 6, 14, 22c, 26

Problems chapter 3 Central Tendencies

Pb. 6.
Find the mean, median, and mode for the set of scores in the following
frequency distribution table.

X f
10 2
9 3
8 5
7 6
6 3
5 1

Pb. 14. A sample of N =5 scores has a mean of M = 12. If one person
with a score of X = 8 is removed from the sample, what will be the value
for the new mean?

Pb. 16. A population of N = 8 scores has a mean of U =20. If one score
is changed from X = 14 to X = 30, what will be the value for the new
mean?

Pb. 22. One sample of n =20 scores has a mean of M =50. A second
sample of n = 5 scores has a mean of M= 10. If the two samples are
combined, what is the mean for the combined sample?

Pb. 24. Identify the circumstances in which the median rather than the
mean is the preferred measure of central tendency.

Pb. 26. One question on a student survey asks: In a typical week, how
many times do you eat at a fast food restaurant? The follwoing
frequency distribution table summarizes the results for a sample of n =
20 studdents .

__________________________
Number of times per week F
______________________________
5 or more 2
4 2
3 3
2 6
1 4
0 3

a. Find the mode for this distribution
b. Find the median for the distribution
c. Explain why you cannot compute the mean number of times sing the
data table.

Chapter 4 Comparing measures of variability

4. Can SS ever have a value less than zero? Explain your answer

6. What does it mean for a sample to have a standard deviation of s =
5? Describe the scores in such of a sample (Describe where the scores
are located relative to the sample mean).

14. A student was asked to compute the mean and standard deviation for
The following sample of n = 5 scores: 81,87, 89, 86, and 87. To
Simplify the arithmetic; the student firs subtracted 80 points from each
Score to obtain a new sample consisting of 1, 7, 9, 6, and 7. The mean
And standard deviation for the new sample were then calculated to be M
= 6 and s = 3. What are the values of the mean and standard deviation?
For the original sample?

22c. For the folllowing sample of n = 7 scores

12, 1, 10, 6, 3, 3, 7

Compute SS, Variance and standard deviation for the sample. (How well
Does your estimate compare with the actual value of s?)

26. Calculate SS, Variance and standard deviation for the following
Sample of n =4 scores: 3, 1, 1, 1. (Note; the computational formula
Works best with this scores)

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#### Solution Preview

Please see the attached word document to see the complete solutions with formulas.

Central tendency and comparing measures variability
Problem: Chapter 3, problems 6, 14, 16, 22, 24, 26; Chapter 4, problems
2, 4, 6, 14, 22c, 26

Problems chapter 3 Central Tendencies

Pb. 6.
Find the mean, median, and mode for the set of scores in the following
frequency distribution table.

X f
10 2
9 3
8 5
7 6
6 3
5 1

ANS:-
a)
x f fx
10 2 20
9 3 27
8 5 40
7 6 42
6 3 18
5 1 5
Total 20 152

mean= 7.6

b)
x f cf
10 2 2
9 3 5
8 5 10
7 6 16
6 3 19
5 1 20
20

The cumulative frequency just above 1/N ie. 10 is 16 and the value of x corresponding to 16 is 7. Therefore median=7

c)
x f
10 2
9 3
8 5
7 6
6 3
5 1

Mode is the value which occurs more frequently in a set of observations and around which the other items of the set cluster densely.In other words, mode is the value of th variable which is predominant in the series.In this case value of x corresponding to the maximum frequency, viz., 6 is 7.
Therefore mode=7

pb. 14. A sample of N =5 scores has a mean of M = 12. If one person
with a score of X = 8 is removed from the sample, what will be the value
for the new mean?
ANS:-
&#8721;X=MxN=12*5=60
If one person with score of x=8 is removed the new total will be 60-8=52 and value of N will be 4
Therefore new mean=52/4=13

Pb. 16. A population of N = 8 scores has a mean of U =20. If one score
is changed from X = 14 to X = 30, what will be the value for the new
mean?

ANS:-
&#8721;X=UxN=20*8=160
If one score is changed from x=14 to x=30 new total will be 160-14+30=176 and value of n will be 8
Therefore new mean=176/8=22

Pb. ...

#### Solution Summary

solution tells us how to find mean, median, mode etc from frequency table

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