Descriptive Statistics

Running Head: DESCRIPTIVE STATAISTICS
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DESCRIPTIVE STATAISTICS
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DESCRIPTIVE STATAISTICS
Psy2530- Problem Set #1
1) The data presented above could be considered a sample or population. Using the
information given in the introductory paragraph, explain to me in what context these 80
data points would represent a population and an example where they would represent a
sample.
Solution: The data represented above can be considered as a population if the study
involves a small group of individuals. For example, the investigation of the existence of
gender difference in the level of psychological well- being among the staff members of a
school. In the scenario of a staff member of a school, if the total number of staff members
in a school is 80, then the data set can be considered as a population. On the other hand, if
the investigation involves gender differences in a school with many students and staff
members, then the data set can be considered as a sample of the whole population in that
school. A sample is a subset of a population (Libman & Zipora, 2010)
2) a) What is the independent variable in this study?
Solution: The independent variable is gender (men or women).
b) What is the dependent variable? Is it a continuous or discrete variable? What is the
scale of measurement for this variable?
Solution: The dependent variable is the level of psychological well- being. The dependent
variable is continuous. The variable is measured on a numerical scale.
3) Construct a frequency distribution table with columns for a) absolute frequencies, b)
cumulative absolute frequencies and c) relative frequencies using all 80 data points.
Create a histogram illustrating the absolute frequencies. Be sure to calculate and
present all measures of central tendency and variability for this distribution, i.e., mean,
median, mode, range, variance, and standard deviation.

DESCRIPTIVE STATAISTICS
Solution: Frequency tables for Women
Frequency table for women shows the number of women for each category of age groups. The
age groups have been divided into classes with a width of 10. The column of “lower limit” below
represents the lower limit of each class that starts from 0, and the “upper limit” shows the upper
limit for each class which starts at 19. The absolute frequency is found by simply counting the
number of individuals whose ages fall in the age bracket (class). Cumulative frequency has been
obtained by adding up the absolute frequencies for each class. Since the total is 80, the
percentage (%) has been obtained by dividing each of the values in the cumulative frequency
column by 80 and multiplying by 100.
Absolute frequency = Count of individuals in each class
Cumulative frequency for class n = Cumulative of class (n-1) + Absolute Frequency of class n.
For example: Cumulative Frequency for class (70-79) = Cumulative Frequency of class (60-69)
+ Absolute Frequency of class (70-79).
That is; 27 + 10= 37
Lower limit Upper Limit Absolute
Frequency
Cumulative
Frequency
Cumulative %
0 19 0 0 0.00%
20 29 0 0 0.00%
30 39 0 0 0.00%
40 49 2 2 5.00%
50 59 7 9 22.50%
60 69 18 27 67.50%
70 79 10 37 92.50%
80 89 2 39 97.50%
90 99 1 40 100.00%
More 0 100.00%
Solution: Frequency tables for Men
Absolute frequency = Count of individuals in each class
Cumulative frequency for class n = Cumulative of class (n-1) + Absolute Frequency of class n.
For example: Cumulative Frequency for class (70-79) = Cumulative Frequency of class (60-69)
+ Absolute Frequency of class (70-79).

DESCRIPTIVE STATAISTICS
That is; 27 + 9 = 36
Lower Limit upper
limit
Absolute
Frequency
Cumulative
Frequency
Cumulative %
0 19 0 0 0.00%
20 29 1 1 2.50%
30 39 2 3 7.50%
40 49 8 11 27.50%
50 59 6 17 42.50%
60 69 10 27 67.50%
70 79 9 36 90.00%
80 89 3 39 97.50%
90 99 1 40 100.00%
More 0 100.00%
Solution: Histograms
The histogram is a pictorial representation of the frequencies of each each clsas. The histogram
represents a representation of class frequency against mid class.
Class width= (Lower Limit + Upper Limit)/2
Class Mid- class Frequency
0-19 9.5 Absolute Frequency
20-29 24.5 0
30-39 34.5 0
40-49 44.5 0
50-59 54.5 2
60-69 64.5 7
70-79 74.5 18
8089 84.5 10
90-99 94.5 2
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