This research is based on the comparisons of measures of central
tendency. This is to find the most appropriate measures for average, using
variance for easy collection of data of middle numbers that are centrally
placed. Data was collected on which the various measures of central tendency
was calculated. These measures were then used to calculate the variance for
each distribution. This study shows that the arithmetic mean is the best
measures of central tendency. It is therefore being recommended for wide usage
as a reliable sample mean for population.
TABLE OF CONTENT
Chapter one: Introduction
Background to the study
Statement of problems
Objective of the study
Significance of study
Limitation of study
Definition of term
Chapter two: Literature review
Chapter three: Methodology
The arithmetic mean
The geometric mean
The harmonic mean
The quadratic mean
Chapter four: Solved problem
Summary, conclusion and recommendation
BACKGROUND OF STUDY
In the study of statistics, descriptive statistics is one of the
main area of statistics. It is concerned with the processing, summarizing,
conclusions and presentation of qualitative and quantitative data. This area is
limited to the data at hand no attempt is made to generalize when to begin
courses in statistics with a discussion of so called descriptive statistics.
That is, method of summarizing masses of numerical data, the graphical display
of such data, procedures for ‘fitting’ data to theoretical model and so on. The
aim of such procedures is that communicating, say to a colleague, the salient
features of a set of numbers you have students. The assumption being that he
does not want to be bothered with all facts which supports your conclusion,
this is a laudable aim.
In addition, most rules o
descriptive statistics depend on what one want to do with ones data, few people
collect data in order to summarize, that they collect data to support
arguments, or they collect data to draw inferences from them. If follow that
the detailed of descriptive statistics should come after the study of
statistical inference. After you know the kind of interference you can make
from set of data, then you will know what calculations to performs, it reduces
data to some form, usually a number that is easily comprehended.
A critical statistical notion
for learners is that of data set as an entity, in other words, developing a
statistical perspective. Holding statistical perspective requires a focus on
the dataset as a collective rather than focusing on individual data values. By
focusing on comparing of measure of central tendency. Would be provided with a
conceptual structure that facilitates a focus on aggregates. Measures of
central tendency are a descriptive statistics. If the value arranged in order
of magnitude, a typical value will lie in the central region. This accounts for
the reason why the measure of location is sometimes referred to as the measure
of central tendency.
BACKGROUND TO THE
Measures of central tendency is
also called measures of location or average. An average is a value that is
typical or representatives of a set of data. Since such typical values tend to
lie centrally within a set of data arranged according to magnitude. Practically
everyone have used the word ‘average’ at one time or the other. By average we
usually mean the ‘normal position., for example it is a common knowledge that
‘average’ age for primary school is between five and six years. Employers and
workers union often quote what each other consider to be the ‘average’ income
of employees but with that of the employer usually higher than that of the
union suggesting that the two parties are often speaking of two different
average though generated from the same body of data. Because of the ambiguity
and the confusion associated with the term ‘average’.
STATEMENT OF PROBLEMS
Measures of central tendency
are usually seen as the easiest part of descriptive statistics because it deals
with day-to-day events. Lack of attention to distributional features of data is
apparent in the dominance of numerical methods for making data comparison.
Selecting and collection of data and finding of average numbers is not
difficult but using terms like houses (real object) and living things seems
difficult. The increased focus on elementary level data analysis and statistics
is evident in the proliferation of statistical ideal in people.
OBJECTIVE OF THE STUDY
At the end of the research, we
should be able to compare measures of central tendency in relation to variance.
We would be able to know which among the measures of central tendency is best
used in with the help of variance.
SIGNIFICANCE OF STUDY
At the end of the research, is
application in the physical world would motivate students to study and apply it
into real life situation.
This study is to also enhance
the teaching and effective learning of this subject as it is taught in
mathematics of an institution of higher learning. This is with special
reference in the university, polytechnics and colleges of education. The study
is also of importance to the statistician, scholars, the government and private
DEFINITION OF TERMS
Measures of central tendency of
a distribution is a values which is typical or representation of the data.
Since such typical values tend to lie centrally within a set of data arranged
according to magnitude, average are also called measures of central tendency.
The most common of measures of central tendency are the mode, the median and
the arithmetic mean, the geometric mean, the harmonic mean and the quadratic
The mode of a set of numbers is
that value which has the highest frequency. It may not exist, and even if it
does it may not be unique. A distribution having one mode is called unimodal.
The median of a distribution is
that number for which the values of the distribution which are less than or
equal to it is the same as the values which are greater than or equal to it. Is
also a set of numbers arranged in order of magnitude (i.e. in an array, is
either the middle value or the arithmetic mean of the two middle values.
The arithmetic mean of a set of
numbers x1, x2, x3, … xn is
their sum divided by n.
The geometric mean (G) of a set
of N positive numbers x1,
x2, x3, … xn is the nth root of
the product of the numbers.
The harmonic mean (H) of a set
of n number x1, x2, x3, … xn is
the reciprocal of the arithmetic mean of the reciprocals of the numbers.
The quadratic mean of a set of
square of number x1, x2, x3, … xn is
their sum divided by n
The relations between the
Arithmetic mean, Geometric mean, and Harmonic mean: The geometric mean of a set
of positive number x1,
x2, x3, … xn is less than or
equal to their arithmetic mean but is greater than or equal to their harmonic
Variance of a set of numbers is
the arithmetic mean of the squares of deviation from the mean of numbers.
TERMS AND CONDITIONS APPLY
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