MEASURE OF CENTRAL TENDENCY

INTRODUCTIONFor practical purpose the condensation

of data set into a frequency distribution and the visual presentation are not enough particularly when two or more different data sets are to be compared. A data set can be summarized in a single value. Such a value usually where in the center and representing the entire data set is a value at which the data have a tendency to concentrate.

The tendency of the observation to cluster in the central part of the data is called Central Tendency and the summary values as a measure of central tendency. Since a measure of central tendency indicates the location or general position of the distribution or the data set in range of observations it is also known as measure of location or position. The measure of central tendency or location are generally known as Average, but in everyday language the average is often understood to refer to the arithmetic mean it is for this reason that when anyone speaks of the average.

CRITERIA OF SATISFACTORY AVERAGERigorously defined.Based on all observation made.Simple to understand and easy to

interpret.Quickly and easily calculated.Amenable to mathematical

treatment.Relatively stable in repeated

sampling experiment.Not unduly influenced by abnormally

large or small observation.

TYPES OF AVERAGES

There are five types of averages.oThe Arithmetic Mean.oThe Median.oThe Mode.oThe Geometric Mean.oThe Harmonic Mean.

THE ARITHMETIC MEANThe arithmetic mean or simply the mean is the most familiar average. It is defined as the value obtained by dividing the sum of all the observation by their number , that is

Formula xX

n

THE MEDIANThe median is defined as a value which divides a data set that have been ordered, into two equals parts, one part comparing of observation greater than and the other part smaller than it, or more precisely the median is a value at or below 50% of the ordered data lie.

Formula2

h nMedian l C

f

The ModeThe mode is defined as a value which occurs most frequent in a set of data , that is it indicates the most common results. A set of data may have more than one mode or no mode at all when each observation occurs the same number of times.

Formula

1

1 2( )m

m m

f fMode l h

f f f f

Prepared by:

MUHAMMAD IRFAN HUSSAIN

Bs 3rd Semester (Regular)

Roll # 39

University Of Sargodha