MEANINGS OF STATISTICS
Numerical Facts Systematically Arranged.
Statistics is the mathematical science of making
decisions and drawing conclusions from data in
situations of uncertainty. It includes collection,
organization and analysis of numerical data.
Statistics of prices, Statistics of road accidents,
Statistics of crimes, Statistics of birth, Statistics
of deaths, Statistics of educational institutions
Statistics is a science, pure and applied, of
creating, developing and applying techniques
such that uncertainty of inductive inferences
may be evaluated.
A numerical quantity calculated from a sample.
When the data analyzed are derived from the
biological sciences and medicine, we use
the term biostatistics to distinguish this
particular application of statistical tools and
Types of Statistics
Descriptive Statistics: Methods of
organizing, summarizing, and
presenting data in an informative
Inferential Statistics: A decision,
estimate, prediction, or generalization
about a population, based on a sample
Population:- The collection of all possible observations
whether finite or infinite, relevant to some characteristic
of interest is called a population. The number of
observations in a finite population is called size of the
population and is denoted by N.
Sample: A sample is a part of a population. Generally
it consists of some of the observation. The number of
observations in a sample is called size of the sample
and is denoted by n.
The numerically recording of information
is called observation/datum.
Data: The set of observations is called data.
It was observed that out of 500 rabbits caught,
300 were females. Is there evidence that more rabbits in
this country are females?
It is a quantity computed from a population if
the entire population is available. Parameters are fixed or
constant quantities and not usually known.
A characteristics that varies from individual
to individual is called a variable. For example age, plant
height, weight, no of plants per plot etc are variables as
they vary from individual to individual.
Quantity which do not vary from individual to
Individual is called constant. e.g. e= 2.71828 , = 3.145
Presenting the numerical information in the form
of number, graphs and tables.
To estimate the population parameter on the basis
of the sample statistic.
The aggregate of units under discussion.
A subset / part of the population.
Types of variables:
Fixed or Mathematical Variable:
A variable may be fixed
or Mathematical when its value can be determined before
hand. e.g. amount of fertilizer to be applied to a plot,
amount of insecticide applied to control insect pests.
A variable may be random when its
value cannot be exactly determined. e.g. yield from a plot
Types of variables:
(1):- Quantitative variable (2):- Qualitative variable.
Quantitative variable:- A variable is called Quantitative
variable when a characteristic can be expressed numerically
such as weight, income, number of children.
Qualitative variable:- If a characteristic is non-numerical
such as sex, colour, general knowledge, honesty, beauty, etc
the variable is called Qualitative/ Categorical variable or
Types of Quantitative variable
1:- Discrete variable 2:- Continuous variable .
Discrete variable:- A variable which can assume some
specific values within a given range is called a discontinuous
or discrete variable. e.g. number of trees in a field, number
of leaves in a tree. A discrete variable takes on values which
are integers or whole numbers.
Continuous variable:- A variable which can assume any
value (fractional or integral) within a given range is called a
continuous variable. For example Height of a plant, the
temperature at a place.
Characteristic that varies form individual to individual
a) Fixed variable b) Random variable
Types of Variable
Capable of assuming a numerical value
Can take all possible values in an interval
Can take only specified values
Not capable of taking numerical measurements
Don’t vary from individual to individual
Scales of Measurement
Measurement: Measurement refer to “Assigning of number to
observations or objects.
Scaling: Scaling is a process of measuring.
Four Scales of Measurements
1. Nominal Scale
2. Ordinal Scale
3. Interval Scale
4. Ratio Scale
Four Scales of
Nominal Scale (Weakest form of measurement)
Nominal: Classifies variables simply in terms of their names
and the categories cannot be ranked. The variable “religion”
with the response categories “Christian,” “Jewish,”
“Muslim,” etc. is an example of a nominal scale of
Rainfall may be classified as
Ordinal Scale (When numbers are allocated in some order)
It includes the characteristics of nominal scale and in addition
has a property of ordering or ranking of measurements.
• Attitude scale Strongly agree, agree, disagree
• Social scale Upper, middle, lower
• Performance of players Excellent, good, fair, poor
Interval: Contains categories in which the actual distances,
or intervals, between categories can be compared. For
example, we can say that the difference between ages 20 and
25 is the same as the difference between ages 50 and 55.
Variables at a ratio scale of measurement are, typically,
those such as age, number of children, etc. The values of
these variables have a real "zero" value.
• Height of plant, weight of students, volume, length,