# 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

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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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:-

∑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:-

∑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