STATISTICS:
Is the science of collecting,
representing, analyzing and interpreting of data to assist in making more
effecting decisions.
Types of statistics
1. Descriptive (method organizing and summarizing information in a
clear and effective way)
2. Inferential
(method
of drawing conclusion about population based on information obtain from sample)
Population: A set of all units of interest in a
particular study
Sample: A
representative part of population is called sample
StatistiC: A numerical
quantity computed from sample is called statistic
ParameteR: A numerical
quantity computed from population is called parameter
Objective of statistics Is to make
inference (drawing result) about a population base upon information contain in a sample.
Data: Raw figure
and facts called Data
Types of
data
·
Qualitative
(Are
observation measure on non-numerical scale e.g eye color, hair color)
·
Quantitative
(Are
observation measure on numerical scale e.g height, weight)
Types of quantitative data
§
Discrete
Data (Whose possible values are countable)
§ Continuous Data (Which may assume any value in an
interval)
3. Primary
Data: The data which are collected first time and are
original in character.
4. Secondary DatA: The data which already collected by some other person and
which passed through any statistical process at least one.
Classification: The process of arranging data in groups or classes according
to resemblance
Frequency distribution: Is a table
showing the number items in each class.
Types of frequency distribution
(i) Discrete (ii) Continuous
Tabulation: Order
arrangement of the data in rows and columns
Range: Difference between maximum
value and the minimum value
$$R=x_m-x_n$$
Mid-Range: Mean of highest and lowest value.
$$\frac{x_m+x_n}{2}$$
Group Data: Compact
form of data
Un-group data: Raw form of
data
Class: grouping of values by which
data is binned for computation of frequency distribution
$$C=1+3.3\log n\;\quad n \;is\; number\; of\; observations$$
Class Interval: The size of each class in which a range
of a variable is divided
$$h=\frac{Range}{Class}=\frac{R}{C}$$
Class Limit: Ending and starting points are not same
Class Boundary: Ending and starting points are same
·
Lower class is found by subtracting 0.5 from lower class limit
and upper found by adding 0.5 in upper class limit.
Commutative frequency: Sum of all previous
frequencies up-to current point
Measure of central tendency
A
single quantity measure which could be used
indicate the center of the distribution
Mean Median Mode
Arithmetic Mean: Sum of all observation divided by number
of observation
ü UN-GROUP DATA
For Sample: $\bar{X}=\frac{\sum x}{n}$
For Population: $\mu=\frac{\sum x}{N}$
For Sample: $\bar{X}=\frac{\sum x}{n}$
For Population: $\mu=\frac{\sum x}{N}$
ü GROUP DATA For Sample: For Population:
Median: Most middle value in the
arrangement data set
ü Un-group data For Odd
For Even
ü Group Data
Mode: The most repeated value in the data set
ü Group Data
Measure of Empirical relationship
·
Distribution is symmetrical if Mean=Median=Mode
·
Distribution is non-symmetrical if Mode=3Median-2Mean
Measure of dispersion: Numerical quantity
that describe the spread of values in data set.
Types of is
dispersion
1. Absolute measure
(Measured the variation present among the observations in the unit of variable)
2. Relative measure
(Measured the variation among the observation relative to their averages)
Variants: Average of squared
deviation from population mean (OR)
Sum of squared
deviation from their mean
ü For Un-group data (sample) (population)
ü FOR GROUP DATA (sample) (population)
STANDARD DAVIATION: Positive square root of variance
PROPERTIES OF VARIANTS AND STANDARD DEVIATION
CO-EFFICIENT OF VARIATION: Ratio of
standard deviation to the mean express in percentage.
·
Large value of C.V indicate the observation has much
spread relation to the size of mean
·
Smallest value of C.V indicate the observation don’t
have wide spread relation to the size of mean.
.
PROBABILITY
ü Numerical
value of uncertainty
·
Probability lies between 0 & 1
·
Probability always positive
·
Probability 0 mean no-occurrence
·
Probability 1 mean always occur
PERMUTATION:
Is any order subset from set of n distinct object (ways of arrangement)
COMBINATION: Is any subset of r objects selected without regard of
any order
RANDOM EXPERIMENT: An experiment may
result in different outcomes even though it is performed under similar
condition.
TRAIL: Any experiment is
performed only once.
Sample
Space: Possible outcomes of random experiment (S).
EVENT: Any part of sample
space (An event may contain one or more outcomes)
SIMPLE EVENT: An event consist of
single out come.
COMPOUND EVENT: Event consist of more
than two outcomes.
EQUALLY LIKELY: Outcomes of sample
space called equally likely if all of them have same change of occurrence.
MUTUALLY EXCLUSIVE: Events are called
mutually exclusive if they do not occur together
EXHAUSTIVE EVENT: When sample space is
partitioning into some mutually exclusive events such that their union is
sample space its self.
TYPES OF PROBABILITY
1) OBJECTIVE: The probability that
an event will occur based an analysis in which each measure is based on a
recorded observation.
TYPES OF OBJECTIVE
·
CLASSICAL PROBABILITY: If random experiment
can produce n mutually and equal
likely outcomes and if m out of
these outcomes are consider favorable occurrence of certain event then
Probability of event is
·
RELATIVE PROBABILITY: If random experiment
repeated large number of times say n under
identical condition and if event A is to observed to occur m
times then probability of an event is defined as
(Also
called statistical and empirical definition of probability)
·
AXIOMATIC PROBABILITY
2) SUBJECTIVE
PROBABILITY: Is a probability derived
from an individual's personal judgment about whether a specific outcome is
likely to occur. It contains no formal calculations and only reflects the
subject's opinions and past experience.
o
CONDITIONAL
PROBABILITY: The probability that Event A occurs, given that
Event B has occurred. The conditional probability of Event A, given Event B, is
denoted by the symbol P(A|B).
PROBABILITY
LAWS
LAW OF COMPLEMENTATION: A mutually exclusive pair of events are
complements to each other if
P(A) + P(A') = 1 (Where P(A') is compliment of event)
ADDITION LAW: The probability that Event
A or Event B occurs is equal to the probability that Event A occurs plus the probability
that Event B occurs minus the
probability that both Events A and B occur.
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
MULTIPLICATION LAW: The
probability that Events A and B both occur is equal to the probability that
Event A occurs times the probability that Event A occurs, given that B has
occurred.
P(A ∩ B)
= P(B) P(A|B)