Topic One: Introduction to Statistics

1.1 Study objectives

By the end of this Topic, the learner should be able to:

a) define the term statistics;

b) distinguish between descriptive statistics and inferential statistics;

c) explain the importance of statistics as a tool for business management;

d) highlight the functions of statistics and

e) state the limitations of statistics.

1.2 Meaning of statistics

Statistics is a distinct mathematical science discipline or subject which is the study of the methods
that are used in the collection, classification, organization, presentation, analysis and interpretation
of data. For example, if one wanted information about performance in Quantitative Techniques
within the last three years, one would seek performance records from the academic division. The
sample records available would be large and this would necessitate arranging performance data
records in a grouped frequency distribution table. The data arranged in frequency tables would then
be used to ease computations, such as mean, median, variance, and then interpreted to give
meaningful information.

Statistics may also be defined as numerical data, which has been, collected from a given source and
for a particular purpose e.g. population statistics from the ministry of planning, Agricultural statistics
from the ministry of Agriculture etc

Statistics may also refer to the values, which have been obtained from statistical calculations e.g. the
mean, mode, median, range e.t.c. (Commonly known descriptive statistics)

Business statistics would therefore focus on the collection, classification, organization, presentation,
analysis and interpretation of data that relates to business operations such as cost, demand, supply,
profits, revenues etc so as to aid in business management.

In the business community, managers must make decisions based on what will happen to such
things as demand, costs, and profits. These decisions are an effort to shape the future of the
organization. If the managers make no effort to look at the past and extrapolate into the future, the
likelihood of achieving success is slim.

1.3 Branches of statistics

Statistics has two main branches namely:

1. Descriptive statistics:
This is a branch of statistics which deals with methods of collection of data, its presentation and
organization in various forms, such as distribution tables, graphs (e.g., ogive, Lorenz curves, etc.),
diagrams (e.g., pie charts) and finding measures of central tendency and measures of dispersion or
spread which are used in the description of data. Managers, CEOs etc. make use of descriptive
statistics in presenting their annual reports, financial accounts and bank statements. Descriptive
statistics is used to present the data in an understandable way, so that a meaningful description can
be made.

2. Inferential or predictive statistics:

This is a branch of statistics which deals with techniques used for analysis of data, making estimates
that lead to predictions and drawing conclusions or inferences from limited information taken on
sample basis and testing the reliability of the estimates or predictions. Inferential statistics is used to
make comparisons or predictions about a larger group, known as population, using information
gathered about a small part of that population called a sample. Inferential statistics answers
questions, such as “what is this data telling us about?” and “what should we do?” Techniques used
are forecasting trends, hypothesis testing, kurtosis, skewness,

1.4 Importance of Business statistics

Statistics is essential tool in business management. For the smooth operation of a business, statistical
data is very useful as follows:

1) Provides stand-alone figures and evidence of substantiated positions that enables the
management to set objectives/ goals that provides a level of certainty to directions to take the
company
2) Enables the management to get summarized values representing large areas under their control
rather than detailed figures thus making management process efficient.
3) Is essential for the making of decisions by management. For example, through the analysis of
current production data, the management will be able to make a decision on the area to improve
so as to improve production

4) Accounting is impossible without exactness. Accountants use statistics to provide information to

shareholders and other business stakeholders regarding business liability.
5) Statistics is essential in auditing. Auditing uses the sampling techniques to determine whether
books of accounts have been prepared and trace sources of errors
6) Forecasting Statistics is very important for business managers when predicting the future of a
business for example if a given business situation involves a dependent and independent
variables one can develop an equation which can be used to predict the output under certain
given conditions. For example, Statistics helps the business person to plan according to market
demand, that is, taste of the customers, supply, price, quality of the products, etc., hence making
decisions after studying the pattern of events say forecasting sales, expenses, advertising for the
products, financial resources, location of the
7) Statistics may be used in making or ordering economic order quantities (EOQ). It is important
for a business manager to realize that it is an economic cost if one orders a large quantity of
items which have to be stored for too long before they are sold. This is because the large stock
holds a lot of capital which could otherwise be used in buying other items for sale. It is also
important to realize that the longer the items are stored in the stores the more will be the storage
costs On the other hand if one orders a few items for sale he will incur relatively low storage
expenses but may not be able to satisfy all the clients. These may lose their customers if the
goods are out of stock. Therefore it is advisable to work out the EOQ which will be sufficient
for the clients in a certain period before delivery. The EOQ will also ensure that minimal costs
are incurred in terms of storage

8) When considering new investment or building a new plant, the management may require
collection and evaluation of data on items such as initial cost, competition and potential profit.
The data enables the management to know if the plant will generate profits or not.

9) Statistics provides a means of measure and control production processes to minimize variations
which lead to error and ensures consistency throughout the process. This enables the
management to save money. For Example, for Quality Control purposes, usually there is a
quality control departments in every industry which is charged with the responsibility of ensuring
that the products made do meet the customers standards e.g. the Kenya bureau of standards
(KeBS) is one of the national institutions which on behalf of the government inspects the
various products to ensure that they do meet the customers specification. The KeBS together
with other control department have developed quality control charts. They use these charts to
check whether the products are up to standards or not.

1.5 Functions of statistics

Statistics can be used for various functions but the most essential include:

1) Presenting data in a definite form which makes the statement logical and convincing.
Numerous figures can be summarized into a single intelligible figure.

2) Statistics reduces the complexity of data. Usually raw data is unintelligible. Using
different statistical measures such as averages, graphs, dispersions, etc can reduce the
complexity of data. The unintelligible data can be made simple and can easily be interpreted
and conclusions drawn.

3) Facilitating comparison. Comparison wouldn’t be possible without the use of the various
statistical measures. Both graphical and numerical measures provide ample scope for
comparison.

4) Establishing trends and tendencies. After studying data over a period of time, a trend can
be established which can help in forecasting. Planners can forecast the future produce in
agriculture, future population by considering present day figures.
 5) Drawing valid conclusions/inferences. Statistical measures can be used to draw
conclusions from a given survey which can be used to evaluate different projects.

6) Testing hypotheses. Statistics can be used to test the truth of new ideas. This helps in
developing new theories.

1.6 Limitation of statistics

1) The methods used in statistics only deal with quantitative attributes of data and leave out the
qualitative ones, that is, the methods are not exhaustive. Quantitative attributes include
figures and facts. They also answer questions, such as “how much”, “how many”, while
qualitative attributes cannot be expressed numerically and this includes integrity, honesty,
intelligence, colour, the statistical methods used cannot bring out these characteristics, hence,
a limitation to statistics.

2) Statistical laws used only apply to the average of a given sample, but when it comes to only
one point or an individual from the same sample, the parameter being measured may deviate
from the average for the sample. These statistical laws apply to only specific conditions and,
therefore, cannot be applied universally. These laws are true on average, for example, one
may say that on average all students who sat for a certain paper passed it. Therefore,
statistics sometimes gives results on averages and not being 100% reliable, hence, a limitation
of statistics.

3) Some statistical methods used cannot be applied to heterogeneous data, that is the sample is
not uniform in all characteristics. For example, one may be interested in collecting data
about the characteristics of a certain tribe from a particular community but some of the
respondents may be living within the same community but from a different tribe and hence
gives incorrect information.

4) In inference statistics, some errors are encountered in statistical decisions. Some methods
used may not ascertain whether an error was made or not. Although it is true for the average
of the sample, the choice of the sample from the population as a whole may be biased. The
information obtained from different samples within the same population may give different
results, hence, a limited on of statistics.

5) The information obtained using statistical data or methods should be interpreted, bearing in
mind the characteristics of the sample from which the data was collected In the absence of
this knowledge about the sample, the information is liable to misuse, that is wrong
interpretations or conclusions may be made. It is, therefore, imperative that the statistics
must be used by experts or statisticians only.

6) Statistical information is not an end in itself; it only provides a means of diagnosing a

problem. Other techniques or methods should be applied to use this obtained information
to derive a solution or conclusion about the identified problem.
 7) There is a misunderstanding that a statistical measure can be used as a measure of the
accuracy of a measurement. Statistics in general, provides an estimate of the minimal error
that might be in the measurement. The actual error can be much greater than the minimal
error. Statistics measure the variability of a measurement, not the accuracy of a
measurement.

NOTE

Statistical enquiry involves data collection, Presentation, Analysis and Interpretation

 Data which may be primary or secondary may be gathered or obtained through various methods
of data collection:
o Experiments o Observation studies
o Sample surveys o Interview method
o Document analysis o Questionnaire method
 After data is collected, it is then presented or organized :
o Graphically through the use of charts and graphs
o Numerically through the use of tables
 Once the data is organized, we can go ahead and analyse it by computing various quantities
(called statistics or parameters) associated with the data. Such quantities may include mean, median
mode, standard deviation, variance etc.
 Once we have performed the analysis, we can finally interpret it by using the information to
make assertions about the real world (e.g. the average student in this class has completed x years
of college).