Statistics

Mathematics II
Bus Math 108
UNIT ONE: STATISTICS
Definition
Statistics is the science of conducting studies to collect, organize, summarize, analyze
and draw conclusions from data. To gain knowledge about seemingly haphazard events,
statisticians collect information for variables, which describe the events.
Statistic refers to a single measure of some attribute of sample that is obtained by
applying a function (statistical algorithm) or manipulation to values of the items,
which are known together as a set of data, according a specific set of procedures.

A variable is a characteristic or attribute that can assume different values. Data are the
values (measurements or observations) that the variables can assume. Variables
whose values are determined by chance are called random variables. A collection of
data values forms a data set. Each value in the data set is called a data value or datum.

TYPES OF STATISTICS
Statistics is sometimes divided into two main areas, depending on how data are used.
The two areas are
• Descriptive statistics
• Inferential statistics

DESCRIPTIVE STATISTICS
Descriptive statistics consists of the collection, organization, summarization and
presentation of data. In descriptive statistics, the statistician tries to describe a
situation with precision of quantitative data collected. The statistician can describe the
data by calculating measure of variability or dispersion.

INFERENTIAL STATISTICS
Inferential statistics consists of methods that use sample results to help make
decision or predictions about a population from where the sample was drawn. It uses
probability, that is, the chance of an event occurring. People who play cards, dice, bingo,
and lotteries win or lose according to the laws of probability.
In inferential statistics, statistician tries to make inferences from samples to population.
A population consists of all subjects (human or otherwise) that are being studied.
Most time, due to the expense, time, size of population, medical concerns, etc. it is not
possible to use the entire population for a statistical study; therefore, researchers use

,samples. A sample is a group of subjects selects from a population. Inferential
statistics consists of generalizing from sample to population, performing estimations
and hypothesis test, determining relationships among variables, and making predictions.

VARIABLES AND TYPES OF DATA
Qualitative or Categorical Variables
Qualitative variables are variables that can be placed into distinct or specific categories,
according to some characteristics or attributes. For example, gender (male or female),
skin colors, eyes colors, religious preferences and geographical location.


Quantitative variables
Quantitative variables are numerical and can be ordered or ranked. For example, age,
heights, weights, body temperature, etc.

Classification of Quantitative Variables
Quantitative variables are numerical and can be classified into two groups:
Discrete variables assume values that can be counted.
Continuous variables can assume all values between two specific values. They
are obtained by measuring.

Classification of Measurement
Measurement refers to the assignment of numbers to objects or events according to
specific set of rules. The broader aspect of measurement is expressed by the type of
measurement or scale used.

• Nominal Scale of Measurement: nominal variables differ qualitatively. For
example, eye colors, political affiliation, religious preferences, gender, etc. are
nominal variables, that can be analyzed by assigning numbers that do not have
any quantitative value. The nominal scale of measurement classifies data into
mutually exclusive (non-overlapping), exhausting categories in which no order or
ranking can be imposed on the data.
Example: Gender (1 = male, 2 = Female); Jessey number (Jessey #4, Jessey #5,
Jessey #10)

• Ordinal scale of measurement: ordinal scale of measurement classifies data into
categories that can be ranked. For example, putting students’ performance on
the scale of excellence, very good, good, fair, poor; class leadership positions:
President, Vice President, Secretary

• Interval scale of measurement: the scale of measurement that has equal

, distances between adjacent numbers as well as ordinality. Examples of Interval
Scales: Time, Temperature, Age, income, volage, etc.
• Ratio scale of measurement: ratio scale of measurement allows researchers to
make ratios as well as ordinal statement because it has equal intervals between
adjacent points on the scale and an absolute zero point. Examples: Weights,
body temperature, heartbeat rate, etc.

TYPES OF FREQUENCY DISTRIBUTION
To describe situations, draw conclusions, as well as make inference about events, the
researcher must organize the data in some meaningful way. The most convenient
method of organizing data is to construct a frequency distribution.

A frequency distribution is the organization of raw data in table form, using classes and
frequencies.
Two types of frequency distribution that are often used are the categorical frequency
distribution and grouped frequency distribution.

CATEGORICAL DISTRIBUTION
The categorical frequency distribution is used for data that can be placed in specific
categories, such as: nominal - or ordinal-level data. For example, data search as political
affiliation, religious affiliation or major field of study we used categorical frequency
distribution. Example 25 army inductees were given a blood test to determine their
blood test the data set is

A B B AB O
O O B AB B
A O O O AB
AB A O B A
O B O O AB

Construct a frequency distribution for the data.

Blood Type Tally Frequency
A
B
AB
O

Example
The following data represent the color of men’s dress shirts purchased in the men’s