MATHEMATICS AS A TOOL
A. Data Management
Data
Data is everywhere. It is observable or measurable. With the advancement of
technology every day, data can be accessed anywhere and by anyone. When data is
correct, valid analysis and interpretation can be generated to produce valuable information.
Gathering and Organizing Data
Data are the quantities Data are the quantities (numbers) or qualities (attributes)
measured or observed that are to be collected and analyzed (Asaad, 2004). There are
two types of data: the qualitative and quantitative data. Qualitative data deals with
categories or attributes. Examples are color of eyes, ethnicity and brand of ice cream.
Quantitative data are numerical data. Quantitative data can be discrete or
continuous. Discrete data is obtained through counting. Continuous data is obtained
by measuring. The number of households in a particular community is an example of
discrete data while family income and weight of an individual are some of the examples
of continuous data.
Another way is to classify data into four levels of measurement such as nominal,
ordinal, interval and ratio. The nominal level of measurement is the lowest of the
four ways to characterize data. Nominal data deals with names, categories, or labels.
Data at the nominal level is qualitative. Colors of eyes, yes or no responses to a survey,
and favorite breakfast cereal all deal with the nominal level of measurement.
Ordinal level of measurement ranks qualitative data. Winners in a pageant and
the academic rank of teachers are examples of ordinal data. Interval level of
measurement deals with data that can be ordered, and in which differences between
the data does make sense. Data at this level does not have a starting point. The
Fahrenheit and Celsius scales of temperatures are both examples of data at the
interval level of measurement. The fourth and highest level of measurement is the
ratio level. Data at the ratio level possess all of the features of the interval level, in
addition to a zero value. Examples are weight, the time to answer a quiz and the number
of absences of students in a class.
Representing using Graphs and Charts; and Interpreting Organized Data
After the data have been collected and processed, data need to be organized to produce
meaningful information. There are three methods in presenting information from the data set.
▶ Textual or paragraph or narrative form
This describes the data by enumerating some of the important feature of the data set
like giving the highest, lowest or the average values. In case there are only few
MATHEMATICS AS A TOOL
observations, say less than ten observations, the values could be enumerated if there
is a need to do so. Data could also be presented using tables.
▶ The tabular method of presentation
This is applicable for large data sets. A frequency is the number of times a value
of the data occurs. A frequency distribution is the organization of raw data in table
form, using classes and frequencies.
A relative frequency is the ratio (fraction or proportion) of the number of times a value
of the data occurs in the set of all outcomes to the total number of outcomes. To find the
relative frequencies, divide each frequency by the total number of students in the
sample. Relative frequencies can be written as fractions, percent, or decimals.
Cumulative relative frequency is the accumulation of the previous relative
frequencies. To find the cumulative relative frequencies, add all the previous relative
frequencies to the relative frequency for the current row.
Example 1
Twenty-five employees were given a blood test to determine their blood type.
Construct a frequency distribution for the data.
Raw Data: A, B, B, AB, O
O, O, B, AB, B
AB, A, O, B, A
B, B, O, A, O
A, O, O, O, AB
Table 1. Frequency Table of Employees Blood Type with Relative Frequencies
Class
A
B
O
AB
Tally
IIII
IIII II
IIII IIII
IIII
Frequency
Relative Frequency (%)
5
7
9
4
n=25
20
28
36
16
100
When the range of the data is large, grouped frequency distributions are used.
The smallest and largest possible data values in a class are the lower- and upperclass limits. Class boundaries separate the classes. To find a class boundary,
average the upper-class limit of one class and the lower-class limit of the next
class. The class width can be calculated by subtracting successive lower-class
limits (or boundaries) or successive upper-class limits (or boundaries). The class
midpoint Xm can be calculated by averaging upper and lower class limits (or
boundaries).
Rules for Classes in Grouped Frequency Distributions
There should be 5-20 classes, the class width must be an odd number, mutually
exclusive, continuous, exhaustive and must be equal in width (except in open-
MATHEMATICS AS A TOOL
ended distributions).
MATHEMATICS AS A TOOL
MATHEMATICS AS A TOOL