Rj Prashant's ppts on statistics

The process of “collecting, organising, presenting, analysing &
interpreting the data” is termed as STATISTICS.
It is a branch of mathematics which deals with 5 observations
or operations related to data specifically.
Branch of science which specially deals with data.
It may be defined as the science of collection, presentation,
analysis and interpretation of numerical data.
(given by Croxton and cowden)………………………..
The science and art of handling aggregate of
facts observing, enumeration, recording,
classifying and otherwise systematically
treating them.
(given by Harlow)

Data (most relevant information only)
 Definition - Any observation that we’ve collected or A
systematic record of facts or different values of a quantity.
 Types - Two types (Basically).
I. Qualitative Data – Uncountable observations. As – ability,
loyalty, etc.
II. Quantitative Data – Countable observations. As – No. of
students, Teachers, etc.
 Series – Data representation.
 Types of series- 3.
i. Individual Series – raw or unmanaged data expression
method; i.e. – 56,35,82,22,1……..
ii. Discrete Series – normally data expression with respect to
that’s frequencies;
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iii. Continuous Series
 Well managed data expression in the form of their
fixed interval.
 There is two types of it, as follows –
 Inclusive Continuous Series- i.e.-
 Exclusive Continuous Series- i.e.-
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Kinds of Statistics
Rj Prashhant
Theoretical Statistics
[purely for maths]
Applied Statistics
Statistical Tests
Descriptive Statistics
Drawing conclusion about a
population based on a data
observed in a sample
Organising,
Summerising and
presenting data.
Hypo. Development Measures of variability
Measures of CT
Inferential Statistics
Mean Median Mode Range Variance Standard
Deviation
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Measures Of Central Tendency
 It is a central as well as typical value for a probability distribution.
 It may also be called a centre or location of distribution.
 Actually it’s a single value that attempts to describe a set of data
by identifying the central value within that set of data.
 Sometimes it’s also known as measures of central location.
 Overall it is defined as the number used to represent the set of
centre or middle data values.
 Its a measure that tells us about where the middle of a bunch of
data lies.
 It will be helpful to create the policies for formors, students &
others.
 The 3 commonly used measures of CT are as follows –
A. Mean,
B. Median &
C. Mode.
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Measures of Variability
 It describes how far a part data point lie from each other and
from centre of distribution.
 Along with measure of CT, it give(s) us descriptive statistics that
summarize our data.
 I represents the amount of dispersion in a data set.
 Almost by the Definition; it is extent to which data points in
statistical distribution or data set diverge-vary from the average
value as well as the extent to which these data points differ from
each other.
 A few measures of variability (are) as follows –
 Range,
 Variance,
 Standard Deviation &
 Standard Error…….
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Mean
 Average value of all the values strongly affected by
extreme values & skewed distribution.
 The average of a data set of values as well as a set of
observation.
 A mean is the simple mathematical average of a
set of two or more numbers.
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Or
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Here; f= frequency,
x= data,
fx= product of frequency
& observation,
AM= Assumed mean.

Median
 Middle most value of an ordered set of values not
affected by extreme values or skewed observation.
 The most common number or observation, which is
given as a set.
 The middle observation from the given data.
 Formula (for grouped data)-
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Here; cf= Cumulative frequency,
l= Lower limit of the modal class,
N/2= half of total observation,
i = class size,
f = frequency.

Mode
 The most common value of the data set.
 The observation having highest frequency.
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Here; f0= highest frequency of the give set,
l= Lower limit of the modal class,
N/2= half of total observation,
i = class size,
f1 = most prev. frequency of f0,
f2 = most forwarded frequency of f0

Applications of Mean, Median and Mode
 Mean, median and mode shows different perspective of
same data.
 Mean gives the average of the observations, where each
observations are given equal importance. It is used to
calculate where all the data is important.
 Median is used to determine a point from where 50% data
is less & 50% is more. It is used where extreme can be
ignored.
 Mode is depended upon the frequency of data, as the
frequency be changed it may be change but when the
frequency remains same w r t to given data we can not
calculate it.

Measures of variability
 Range - The difference between highest and lowest
score.
 Class Mark – mid value of the two limits of the class.
 Frequency distribution table – table that shows the
frequency of different values in the given data.
 Ungrouped Frequency distributn Table
 Grouped Frequency distribution table
X- Axis – Abscissa
Y- Axis - Ordinate

 Bar Graph - It is a pictorial representation of data in
which rectangular bars of uniform width are drawn
with equal spacing between them on one axis, usually
the x axis.
 Abscissa contains the class intervals
 Ordinates contain the frequency with respective gap in
it.
 Histogram – It is a set of adjacent rectangles whose
area are proportional to the frequencies of a given
frequency distribution.

Bar graph

Histogram

Deviation
 deviation is a measure of difference between the observed
value of a variable and some other value, often that
variable's mean.
 The sign of the deviation reports the direction of that
difference (the deviation is positive when the observed
value exceeds the reference value).
 The magnitude of the value indicates the size of the
difference.
 Formula – deviation(d) = x – (calculated)mean
 The sum of deviation from mean is always be zero (0), as
it’s a property of sample mean.
 The sum of the d, below the mean will always be equal the
sum of d above the mean.

Standard Deviation

Rj Prashant's ppts on statistics

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