CHAPTER THREE
ORGANI
ZATION OF DATA
3.1Introduc
tion
Desc
ri
ptive statist
ics is one ty
pe of
statist
ics, which involved dat
a collection, presentation and
description of numerical data.
Data collected in education can
be generated through many sourc
es, ranging from test scores,
frequencies, opinions, etc.
thus the process of re-organ
izing research data in such
way as to make them meaningful and useful is known as data organization.
In data organization, can be grouped in ascending order, descending order and frequency table for comprehension.
3.2Objectives
At the end of this chapter, readers should be able to:
arrange data in order of magnitude
arrange data in tabular form
arrange data in frequency distribution table
3.3Sequencing
The data arranged in order of magnitude is either in ascending or descending order.
Example 1:
Given that 10 students have the following scores in mathematics test: 5, 8, 13, 18, 12, 15, 6, 9, 7, 20
The ascending order gives: 5, 6, 7, 8, 9, 12, 13, 15, 18, 20
While the descending order gives: 20, 18, 15, 13, 12, 9, 8, 7, 6, 6, 5
Note that when data collected consist of names, they can be arranged in alphabetical order.
But when the data consists of objects, animals, event, etc., you may arrange based on its kinds or groups.
3.3.1Rank Order
If the data obtained shows rank order, it sometimes may be described with descriptive statistics such as histograms, pie chart, frequency polygon, and bar charts. To illustrate this order, considering the scores on an intelligence mathematics test for six students.
Table 1. Rank Order in Test Scores
Students | Score | Rank |
1 | 153 | 1 |
2 | 142 | 2 |
3 | 140 | 3 |
4 | 127 | 4 |
5 | 118 | 5 |
6 | 109 | 6 |
The scores can be rank order from the most intelligent to the list intelligent as been carried out in Table 1. In other way, it could be ranked from least scores to highest intelligent, assignably 109 to be rank of 1, the intelligent test score of 118 be assigned as rank of 2, and so on.
3.4Tables
The data collected can be organized or arranged in a Table either by categories or frequencies. An example of a two-dimensional representation of statistical data is a table. Table must have general title, column title and row title, with a source note on it bottom.
For example, academic planning unit C. O.E Minna has on their records numbers of students admitted from 2010 to 2016, and distribution of Lecturers in each department as at year 2022.
Example 1
Table 2: Students’ Admission in Niger State College of Education, Minna, 2010–2017
S/N | Year | Males | Females | Total |
1 | 2010 | 1200 | 1050 | 2250 |
2 | 2011 | 1557 | 1400 | 2957 |
3 | 2012 | 1300 | 1150 | 2450 |
4 | 2013 | 1600 | 1400 | 3000 |
5 | 2014 | 1504 | 1335 | 2839 |
6 | 2015 | 1706 | 1540 | 3246 |
7 | 2016 | 1245 | 1150 | 2395 |
Source: Academic Planning & Statistics Units.
Example 2
Table 3: Distribution of Lecturers in School of Sciences
S/N | Department | No. of Lecturers |
1 | Biology | 15 |
2 | Chemistry | 10 |
3 | Computer Science | 06 |
4 | Integrated Science | 11 |
5 | Mathematics | 12 |
6 | Physical and Health Education | 18 |
7 | Physics | 07 |
Total | 79 |
Source: Dean’s office.
3.5Frequency Distribution Table
Basically, there are two kinds of frequency distribution tables; ungrouped and grouped frequency distribution tables. These tables display the frequency with which each value, item, or score appears in a certain distribution. The frequency table is used as a means of summarizing and highlighting important aspect of mass data in a more meaningful and interpretable form. It consists of three columns, score/items, tally mark and frequency.
3.5.1 Ungrouped Frequency Distribution Table
In organizing and presenting data of ungrouped data by a Researcher, there are some procedures to be followed. These procedures are:
Step 1:Arrange the items or scores in ascending or descending order.
Step 2:In column 2, tally each item or stroke for each time you come across the item or score in the array. The fifth time cross the four strokes already put down.
Step 3:Write number of strokes for each item or score in third column. To illustrate the organization and presentation of ungrouped frequency distribution table, let us look into the following examples.
Example 3.
The followings are test scores of students in 2nd semester Examination
20, 30, 10, 20, 20, 10, 30, 30, 30, 10, 60, 70, 40, 30, 30, 80, 60, 50, 90, 60.
Table 4: Test Scores of Students Examination
Score X | Tally Marks | Frequency |
10 | III | 3 |
20 | III | 3 |
30 | IIII I | 6 |
40 | I | 1 |
50 | I | 1 |
60 | III | 3 |
70 | I | 1 |
80 | I | 1 |
90 | I | 1 |
Total | 20 |
Example 4.
In a study of opinion of Pre-service Mathematics Teachers’ Efficacy of Problem-solving Attitude on Achievement in Mathematics in Niger State College of Education, Minna. The following score of 30pre-service teachers were obtained for two items in Problem-Solving Attitude Questionnaire (PSAQ). The questionnaire developed is on five-point scale: Strongly Agree (SA) = 5, Agree (A) = 4, Disagree (D) = 3, Strongly Disagree (SD) = 2, Undecided (U) = 1.
Table 4.1. Scores obtained by 30 Pre-Service Teachers on the Two Items
S/N | Item | SA | A | D | SD | U |
5 | 4 | 3 | 2 | 1 | ||
1. | Most people think that I am objective and logical | 7 | 10 | 8 | 2 | 3 |
2. | I really enjoy solving new problems | 12 | 6 | 4 | 6 | 2 |
As a Researcher, you need to know the number of responses in each item. To carry out this, you need to prepare an ungrouped frequency distribution table and can be presented in Table 4.2 and 4.3
Table 4.2: Ungrouped Frequency Distribution Table for 30 pre-service teachers for item I: “Most people think that I am objectives and logical”
Table 4.2: 30 Pre-Service Teachers on Item One
Scores | Tally | Frequency |
5 | IIII II | 7 |
4 | IIII IIII | 10 |
3 | IIII III | 8 |
2 | II | 2 |
1 | III | 3 |
Total | 30 | |
Table 4.3. Ungrouped Frequency Distribution Table for 30 Pre-service Teachers on Item 2: “I really enjoy solving new problems”, can be shown as below:
Scores | Tally | Frequency |
5 | IIII IIII II | 12 |
4 | IIII I | 6 |
3 | IIII | 4 |
2 | IIII I | 6 |
1 | II | 2 |
Total | 30 | |
3.5.2 Grouped Frequency Distribution Table
A Researcher may obtain large number of scores and may be very difficult to list all of them. For easy and faster approach is good to group the scores. To prepare a grouped frequency distribution table, you need to adopt the following steps:
Step 1: Grouping the scores into class intervals.
Before the grouping, it is worthy to understand some basic concepts involved. These are class interval, class size, class limits and class boundaries.
A class interval is a small group of score within uniform scores in each group. Two extreme scores are involved, the lowest scores and highest score. While the number of scores within a class interval is known as the class size. The extreme scores in a given class interval is known as a class limit. The highest score is upper class limit, and lowest score is lower class limit. For example, a class interval 3–6, the class size is 4. The lower-class limit is 3 and 6, is the upper-class limit.
Also, class mark (class mid-point) is obtained by adding the lower and upper-class limits, divided by two. Thus, the class mark of the class interval 3—6 is \\frac{3+6}{2}=4.5
Class boundaries is obtained by adding 0.5 to the upper-class limits and subtracting 0.5 from lower class limit. From the class interval 3 - 6, the lower-class boundary is 2.5 and upper-class boundary is 6.5. Below shows some class limits and their corresponding class boundaries.
Table 4.4:
Class Limit | Class Boundaries |
3—6 | 2.5—6.5 |
7—10 | 6.5—10.5 |
11—14 | 10.5—14.5 |
15—18 | 14.5—18.5 |
19—22 | 18.5—22.5 |
The Researcher must determine the class size to be used before grouping the score. To carry out that you require the following procedures:
Step 1: The range of the set of scores between the highest score and lowest score is determined.
Step 2: Range is divided by 10, you usually have between 10 to 15 classes of scores (groups).
Step 3: The result obtained is approximated to the nearest odd number.
Step 4: Tally the score in column 2.
Step 5: Put down the frequency occurrence of each class interval in column 3.
Let us illustrate with the data obtained by a researcher after administered post-test in a study.
45 22 33 51 34 22 66
40 37 42 46 29 41 33
38 47 43 39 57 65 38
44 31 11 38 45 32 41
57 59 46 25 54 39 40
42 62 35 17 43 55 20
53 57 37 43 32 27 45
Step 1: Group the scores into class intervals. To do this, you need to determine the class size. In determining the class size, you should ensure that the number of class intervals are not fewer than 10 or more than 20. Class size should be at 2, 3, 5, - - - 10 and multiples of 10 are preferred.
From the data above, lowest score is 11. Let arrange 6 classes of 10 class size.
The grouped frequency distribution table for the data above is presented in Table 5.
Table 5: Data for Post-test Score in Examination
Class Interval | Tally | Frequency |
10—19 | II | 2 |
20—29 | IIII I | 6 |
30—39 | IIII IIII IIII | 14 |
40—49 | IIII IIII IIII II | 17 |
50—59 | IIII III | 8 |
60—70 | III | 3 |
Total | 50 | |
Student Activity
Why are statistical data put into tables?
How many types of tabulation are there? Name them.
What is frequency distribution tables?
How many kinds of frequency distribution tables are there? Name them.
What are the characteristics of general statistical table?
Explain the following concepts:
Class interval,
Class mark
Upper class limits
Lower class limit.
The following table lists some students’ MAT 203 exam results. Create a frequency distribution table with the scores.
20, 25, 28, 22, 24, 25, 30, 25, 26, 21, 22, 24, 29, 30, 27, 28, 25, 23, 21, 22, 29, 23, 20, 24, 27, 29, 26, 25, 25, 25.
A Researcher conducted a study and administered post-test. The scores are presented below, organize the results into a frequency table.
55, 39, 48, 60, 46, 52, 51, 33, 58, 65, 55, 62, 59, 53, 50, 55, 52, 48, 58, 65, 60, 55, 60, 51, 35 36 55, 54, 68, 68, 55, 45, 55, 52, 62, 56, 59, 47, 39, 46, 60, 58, 65, 33, 42, 53, 40, 47, 34, 61, 42, 48, 38, 48, 50.
References
Adamu, S.O & Johnson T. I. (1975). Statistic for Beginners Onibonoje Press and Book Industries (Nig) Ltd.
Awotunde, P.O & Ugodulunwa (2002). An Introduction to Statistical Methods in Education. Printed and published in Nigeria by Fab Anieh (Nig) Ltd.