1. Describing and Organizing Data
PSYSTA1 – Weeks 3-4

2. RAW Data
the data set in its original form, wherein the recording process is done in the sequence in which they are collected

3. PRESENTING and SUMMARIZING Data
Tables
Graphs
Numerical Measures
oftentimes accompanied by textual presentations

4. TABLE
systematic organization of data in rows and columns

5. TABLE
GUIDELINES:
The title should be concise and not in complete sentence.
Column labels should be precise.
The units of measurements must be clearly stated.
Show any relevant total, subtotals, percentages.
Indicate if data were taken from another publication by including a source note.
Tables should be self-explanatory.
It may be accompanied by text.

6. FREQUENCY DISTRIBUTION
presents the score values and their frequency of occurrence
an organized presentation of the number of individuals located in each category on the scale of measurement
presents a picture of how the individual scores are distributed on the measurement scale
may be structured either as a table or as a graph
In any case, the following elements are presented:
the set of categories that make up the original measurement scale
a record of the frequency, or number of individuals in each category

7. FREQUENCY DISTRIBUTION Table
Two (2) Types:
Single Value Grouping
usually for qualitative or (limited) discrete quantitative data

8. Some DEFINITIONS Relative Frequency Percentage
indicates the proportion of the total number of items that occurs in each interval category
= frequency total number of observations
Percentage
indicates the relative frequency presented in parts per 100
=relative frequency×100%

9. Example 1
Fifty first year college students were asked about their favorite electronic gadget: iPad, PlayStation Portable or PSP, iPhone, camera, iPod. Below is a list of their responses. Construct a frequency distribution table for this data set.

10. (2-way) CONTINGENCY Table
a statistical table that shows the observed frequencies or proportions of data elements classified according to two variables, with the rows indicating one variable and the columns indicating the other variable
a table showing the contingency between two variables where the variables have been classified into mutually exclusive categories and the cell entries are frequencies

11. (2-way) CONTINGENCY Table

12. FREQUENCY DISTRIBUTION Table
Two (2) Types:
Grouping by Class Interval
usually for quantitative data

13. Some DEFINITIONS Class Mark/Midpoint Cumulative Frequency
midpoint (average) of the upper and the lower real limits (boundaries) of each interval
𝑪𝑴= 𝐥𝐨𝐰𝐞𝐫 𝐥𝐢𝐦𝐢𝐭+𝐮𝐩𝐩𝐞𝐫 𝐥𝐢𝐦𝐢𝐭 𝟐
Cumulative Frequency
indicates the number of scores that fall below the upper real limit (boundary) of each interval
Cumulative Percentage
indicates the percentage of scores that fall below the upper real limit of each interval

14. FREQUENCY DISTRIBUTION Table
STEPS: (Grouping by Class Interval)
Find the range (max – min) of the scores.
Determine the width of each class interval w.
𝒘= 𝐫𝐚𝐧𝐠𝐞 # 𝐨𝐟 𝐜𝐥𝐚𝐬𝐬𝐞𝐬
List the limits of each class interval, placing the interval containing the lowest score value at the bottom.
Tally the raw scores into the appropriate class intervals.
Add the tallies for each interval to obtain the interval frequency.

15. Example 2
Given the following 90 scores, construct a frequency distribution of grouped scores having approximately 12 intervals.

16. EXERCISE
The psychology department of a large university maintains its own vivarium of rats for research purposes. A recent sampling of 40 rats from the vivarium revealed the following rat weights (grams): Construct a frequency distribution of grouped scores with approximately 10 intervals.

17. GRAPH
a device for showing numerical values or relationships in pictorial form

18. GRAPH
Advantages:
main features and implications of a data can be easily grasped
can attract attention and hold the reader’s interest
simplifies concepts that would otherwise have been expressed in so many words
can readily clarify data, frequently bring out hidden facts and relationships

19. Qualities of a GOOD Graph
Accurate
should not be deceptive, distorted, or misleading
Simple
should be straightforward, not loaded with irrelevant or trivial symbols and ornamentation
Clear
should be easily read and understood
Appearance
to attract and hold attention

20. LINE Graph
useful for showing trends over a period of time

21. PIE Chart
a circle is divided into sectors in such a way that the area of each sector is proportional to the size of the quantity represented by that sector

22. PICTOGRAPH
pictures or symbols are used to represent certain quantity or volume

23. MAP Chart
displays data by shading sections of a map, and must include a key; a total data number should be included

24. DOT Plot
a plot of points along a single axis (usually the horizontal axis) which represents a countable scale and when data values repeat, the dots are placed above one another, forming a pile at that particular numerical location

25. BAR Graph
consists of a series of rectangular bars where the length of the bar represents the magnitude
the bars for each category do not touch each other, emphasizing the lack of a continuous relationship between the categories

26. Example 3
Construct a bar graph for the “electronic gadget data” presented in Example 1.

27. HISTOGRAM
class limits (boundaries) are represented by the width of the bars and the frequencies that fall within the classes are represented by the height of the bars
bars are drawn adjacent with one another to emphasize continuity of the underlying measurement

28. FREQUENCY Polygon
points plotted over the midpoint of each interval at a height corresponding to the frequency of the interval are joined with straight lines, while the line joining the points is extended to meet the horizontal axis at the midpoint of the two class intervals falling immediately beyond the end class intervals containing scores (hence, a polygon)

29. OGIVE (CUMULATIVE Curve)
a graph showing the curve of a cumulative distribution function (either frequencies or percentages) wherein the points plotted are the upper class limit and the corresponding cumulative distribution

30. Example 4
Construct a histogram, a frequency polygon, and an ogive for the given data in Example 2. Be guided by the constructed FDT.

31. STEM-and-LEAF Display
a device for presenting quantitative data in a graphical format by splitting each data value a “leaf” and a “stem”

32. STEM-and-LEAF Display
STEPS:
Divide each measurement into two parts: the stem and the leaf.
List the stems in a column, with a vertical line to their right.
For each of the measurement, record the leaf portion in the same row as its corresponding stem.
Order the leaves from lowest to highest in each stem.
Provide the key to your stem and leaf coding so that the reader can recreate the actual measurements if necessary.

33. Example 4
Construct a stem-and-leaf display (with stem unit = 10 and leaf unite = 1) for the data given in Example 2.

34. Some Notes on STEM-and-LEAF Display
first developed in 1977 by John Tukey, working at Princeton University
a simple alternative to the histogram and are most useful for summarizing and describing data when the data set is small
it does not lose any of the original data (unlike the histogram)
rotating the stem-and-leaf display 90° counterclockwise, such that the stems are at the bottom, results in a diagram very similar to the histogram

35. EXERCISE
The psychology department of a large university maintains its own vivarium of rats for research purposes. A recent sampling of 40 rats from the vivarium revealed the following rat weights (grams): Construct a histogram, a frequency polygon, and an ogive for the given data. (*Superimpose all three in one graphing plane.)