STATISTICS I DESCRIPTIVE STATISTICS

1. FREQUENCY DISTRIBUTIONS, GRAPHING, AND
DATA DISPLAY
SUMMARIZING DATA
Desmond Ayim-Aboagye, PhD

2. SUMMARIES
•Tables
•Figures
•Graphs
•What do these teach us?

3. 0
1
2
3
4
5
6
Category 1 Category 2 Category 3 Category 4
Chart Title
Series 1 Series 2 Series 3
Figures 1. Graphs

4. 0
0.5
1
1.5
2
2.5
3
3.5
0 0.5 1 1.5 2 2.5 3
Y-Values
Figure 2. Graphs
0
0.5
1
1.5
2
2.5
3
3.5
0 0.5 1 1.5 2 2.5 3
Y-Values

5. Type 1 Type 2
40 30
50 40
60 50
Table 1, Type 1 and Type 2

6. Sales
1st Qtr 2nd Qtr 3rd Qtr 4th Qtr
Figure 3, Sales

7. Their Importance are that:
• Educate and encourage viewers to think about relationships within
data.
• Sometimes such summaries can spark controversies, leading to
creative insights about behavior

8. Frequency distribution
• Research Methods for Collecting Data
• Experiment
• Correlational study
• Quasi-experiment
• 1). Code them 2). Convert them to numbers to enable analysis

9. Scales of Measurement (chapt.1)
• 1. Nominal
• 2. Ordinal
• 3. Interval
• 4. Ratio
• How do we organize and summarize them?

10. Frequency distribution
• A frequency distribution is a table presenting the number of
participant responses (e.g., scores, values) within the numerical
categories of some scale of measurement.

11. Respondents and their agreement or
disagreement
• “Mathematics is my favorite course this semester” [five-point interval]
(In the case of 8 items, the scores can range from 8 to 40)
• I strongly agree, 5
• I agree, 4
• I strongly disagree, 3
• I disagree, 2
• I neither agree or disagree, 1
• I don’t know, 0

12. x f fx
40
39
38
37
36
35
34
33
32
31
30
29
28
27
26
25
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
1
0
0
0
1
1
1
2
1
1
2
1
0
1
0
1
0
0
5
1
1
1
0
1
0
0
1
0
1
0
4
40
0
0
0
36
35
34
66
32
31
60
29
0
27
0
25
0
0
110
21
20
19
0
17
0
0
14
0
12
0
40
(40 x 1 = 40)
( 39 x 0 = 0 )
( 38 x 0 = 0)
( 37 x 0 = 0)
(36 x 1 = 36)
( 35 x 1 = 35)
( 34 x 1 = 34)
( 33 x 2 = 66)
( 32 x 1 = 32)
( 31 x 1 = 31)
( 30 x 2 = 60)
( 29 x 1 = 29)
( 28 x 0 = 0)
(27 x 1 = 27)
( 26 x 0 = 0)
( 25 x 1 = 25)
( 24 x 0 = 0)
( 23 x 0 = 0)
(22 x 5 = 110)
(21 x 1 = 21)
( 20 x 1 = 20)
( 19 x 1 = 19)
(18 x 0 = 18)
(17 x 1 = 17)
( 16 x 0 = 0)
( 15 x 0 = 0)
(14 x 1 = 14)
( 13 x 0 = 0)
( 12 x 1 = 12)
(11 x 0 = 0)
( 10 x 4 = 40)
Table 3.2 Frequency Distribution for Life Orientation Test (LOT) Scores

13. Frequency data
• Frequency distributions simplify data for quick study. When they are
constructed well, no valuable information is lost.
• Suppose N = 30
• Scores = x
• Σ𝑓 = N
• Σ𝑓.x = Σ𝑓𝑥
• See Table 3 in your book

14. Proportion and percentages
• A proportion is a number reflecting a given frequency (f)
relationship to the N of the available sample or group. It is a
fractional value of the total group associated with each individual
score.
• Proportion = p= f/N
• that is frequency divided by total number of the group or sample
N (1÷30 =0.033)
• It percentage 0.033 x 100 = 3%

15. Relative frequency distribution for LOT scores
• P = f/N adding all gives 1.00
• P (100) = 100%
• A relative frequency distribution indicates the percent or
proportion of participants who received each of the raw scores of
x.

16. Class Intervals of x f
37-40
33-36
29-32
25-28
21-24
17-20
13-16
9-12
5-8
1
5
5
2
6
3
1
6
1
Σ𝑓 = 30
Table 3.5 Revised Group Frequency Distribution for LOT Scores
Note: The Intervals in this table are based on the frequency distribution shown in Table 3.2, which in turn is
based on the raw scores from Table 3.1.

17. Class Intervals of x f
36.5-40.5
32.5-36.5
28.5-32.5
24.5-28.5
20.5-24.5
16.5-20.5
12.5-16.5
8.5-12.5
4.5-8.5
1
5
5
2
6
3
1
6
1
Σf = 30
Table 3.6 Grouped frequency distribution of LOT scores with true limits and class
intervals
Note: The intervals in this table are based on the frequency distribution shown in
Table 3.2, which in turn is based on the raw scores from Table 3.1.

18. Constructing Intervals and Scores
• Caution
• Are all the class intervals the same width? They should be the
same.
• Do any class intervals overlap with one another? They should not.
• Do all data fit into the table? There should be no leftover scores.

19. Graphing Frequency Distributions
• A graph is a diagram illustrating connections or relationships
among two or more variables. Graphs are often made up of
connecting lines or dots.

20. Figure 3.2 The Two Axes (x and y) used for graphing data
Higher values for y
Y Axis or Ordinate
Lower values for y
y
Lower values for
x
X Axis or
Abscissa Higher values for
x
x

21. 0
2
4
6
8
10
12
14
Female Male Heterosexual Homosexual
Bar Graphs
Series 1 Series 2 Series 3
Figure 1. Bar graphs of surveys returned by respondents
gender
Y
X

22. 0
2
4
6
8
10
12
14
Year 1 Year 2 Year 3 Year 4
Figure 1. Graph comparing the prices of 3 commodities in 4 years
Pinaples Tobacco Sugar Cane
Prices in
Thousand
Dollars
X axis
Y
axis

23. SHAPE OF DISTRIBUTIONS
• Frequency distributions can come in any number of varieties shapes. But only one is
ideal for performing statistical analyses.
• Normal distribution.
• A normal distribution is a hypothetical, bell-shaped curve wherein the majority of
observations appear at or near the midpoint of the distribution.
• Skew distribution
• This refers to a non-symmetrical distribution whose observations cluster at one end.

24. Skinny and quasi-normal
(leptokurtic)
Normal (mesokurtic) Fatter curve (platykurtic)

25. A positively skewed distribution
A bimodal distribution
Negatively skewed distribution

26. Percentiles and Percentile Ranks
• A Percentile rank is a number indicating what percentage of scores
fall at or below a given score on a measure.
• A score of 75% of an exam is a bout ¾. So when an individual gets
30 score of the exams which is 75% (i.e., ¾) we say that she had
75th percentile.

27. Cumulative Frequency
• A Cumulative frequency refers to the number of values within a
given interval added to the total number of values that fall below
that interval.
• Cumulative frequencies are organized into what are called
cumulative frequency distributions.

28. Class
Intervals of X
f Cf % C%
36.5-40.5
32.5-36.5
28.5- 32.5
24.5- 28.5
20.5- 24.5
16.5- 20.5
12.5- 16.5
8.5- 12.5
4.5- 8.5
1
5
5
2
6
3
1
6
1
30
29
24
19
17
11
8
7
1
3.33
16.67
16.67
6.67
20.00
10.00
3.33
20.00
3.33
100
96.67
80.00
63.33
56.67
36.67
26.67
23.33
3.33
Σ𝑓 = 30
Table 3.9 Cumulative Frequency Distribution of LOT Scores with Limits and Class
Intervals

29. Cumulative Percentage
• Cumulative Percentage = cumulative frequency/total no of scores
x100
• Example cf of 17 will be 17/30 x 100 = 56.67%

30. Quartile
• Q 1, Q 2, Q3, and Q3.
• When a data distribution is divided into four equal parts, each
part is labeled a quartile.