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Introduction & Key Statistical measure

STATISTIC
 The

term statistics is used in two sense:
plural and singular
 As a plural nouns it refers to numerical
statement of facts or a quantitative data
pertaining to a phenomenon  descriptive
statistic
 As a singular nouns, the term “statistics”
refer to statistical methods or methodology
of collecting, compiling, presenting,
analyzing and interpreting quantitative data

COMMON TERMS USED IN STATISTICS
 Variables

are characteristic or attributes
that can be expected to differs from one
individual to another
 Data are used as measurements or
observation of a set of variables
 Population is a collection of
person/objects/item of interest
1

 Sample

is a part of population that
examined in order to gather information
...

 Therefore, statistics is used to make
inference about parameters
...
It provide simple
summaries about sample and the
measures using frequency counts
range, mean, modes, median
scores, and standard deviation

Is used when draw a conclusions
about population based on data
from a sample
...
Random sampling
help to achieve this
...
g
...
e
...

 Discrete:
 Continuous:

3

LEVEL OF MEASUREMENT
 Nominal level: used to classify or categorise
...

 E
...

 E
...
:
 Interval level: an ordered scale in which the difference between measurements is a
meaningful quantity that does not involved a true zero points
...
g:
 Ratio level: like interval scale except it has true zero point
...
g:

All qualitative attributes are either nominal or ordinal
All quantitative attributes are either interval or ratio

4

ORGANIZING AND PRESENTING DATA
 Raw data give very little information
 Data should be condensed and presented in a meaningful way using tables, graphs,
and chart
 Categorical data could be presented as tabulating data (frequency, percentage,
crosstabulation) or graphing data (bar, pie, pareto diagram)

5

NUMERICAL DESCRIPTIVE MEASURE
•

Interquartile range

Mean
Central
tendency

Median
Mode
Quartiles

Numerical
descriptive
measure

Shape

symmetrical
Non-symmetrical
Range
Interquartile range

Variation/Dispersion
Variance and standard
deviation
Coefficient of variation

CENTRAL TENDENCY
 Arithmetic

mean : average of a group of

number
Referring to sample values denoted as x
 Referring to population values, demoted
as μ
 Formula:


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x
n = sample size

N = population size
 Median

: the middle value in an ordered
array of numbers
 Mode : the most frequently occurring
value in a set of data
there could be no mode or may even
there be more than one mode
 unaffected by extreme values




Quartiles: divide the group into
quarters


formula : p × (n+1); p is quartile, n is
number of data

7

VARIATION/DISPERSION


Range : difference between the largest
value of database and smallest value


very sensitive to extreme values

Interquartile range : range between
Q3 and Q1
 Variance and Standard Deviation:




variance = measure of how far a set of
numbers is spread out

 standard

deviation : variation or
"dispersion" exists from the
average (mean)

8

 coefficient

of variation: relative measure
of variation


coefficient of variation =
standard deviation
x 100
mean

MEASURE OF SHAPE


symmetrical distribution have the
identical data value above and below the
mean
 if not, it is called non-symmetrical thus its
either skewed to the left (negative) or to
the right (positive)

meannegatively skewed

9

mean=median=mode
symmetrical

modepositively skewed

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COVARIANCE AND COEFFICIENT OF
CORRELATION
 covariance

is a measure of linear
relationship between two variables
...
value of r is
between -1 (perfect negative
correlation) or +1 (perfect positive
correlation)

12



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Title: Introduction & Key Statistical measure
Description: Statistics for economics & business

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