Statistics XII Math Project.pdf

Statistics
Submitted by-
Pushpadant .R.Patil
Submitted to-
Venu Gopal Sir

What is Statistics?
Statistics is a branch of mathematics that
deals with the collection, review, and analysis of
data. It is known for drawing the conclusions of
data with the use of quantiﬁed models.
Statistics can be deﬁned as the study of the
collection, analysis, interpretation,
presentation, and organization of data. In
simple words, it is a mathematical tool that is
used to collect and summarize data.

Real-life examples of statistics
are given below:
● To ﬁnd the mean of the marks obtained by each
student in a class of 40 students, the average
value is the statistics of the marks obtained.
● Suppose you need to ﬁnd the number of
employed citizens in a city. If the city has a
population of 10 lakh people, we will take a
sample of 1000 people. Based on this, we can
prepare the data, which is the statistic.

Basics of Statistics
Statistics consist of the measure of central tendency
and the measure of dispersion. These central tendencies
are actually the mean, median, and mode and
dispersions comprise variance and standard deviation.
Mean is defined as the average of all the given data.
Median is the central value when the given data is
arranged in order. The mode determines the most
frequent observations in the given data.
Variation can be defined as the measure of spread
out of the collection of data. Standard deviation is
defined as the measure of the dispersion of data
from the mean and the square of the standard
deviation is also equal to the variance.

Mathematical Statistics
The most common application of Mathematical statistics is the
collection and analysis of facts about a country: its economy, and,
military, population, number of employed citizens, GDP growth, etc.
Mathematical techniques like mathematical analysis, linear
algebra, stochastic analysis, differential equation, and
measure-theoretic probability theory are used for different
analytics.

Scopes Of Statistics
Statistics can be used in many major ﬁelds such as
psychology, geology, sociology, weather forecasting,
probability, and much more. The main purpose of statistics is
to learn by analysis of data, it focuses on applications, and
hence, it is distinctively considered as a mathematical
science.

Methods in Statistics
The statistical process involves collecting, summarizing, analyzing, and
interpreting variable numerical data. Some methods of statistics are given
below.
● Data collection
● Data summarization
● Statistical analysis

What is Data in Statistics?
Data can be deﬁned as a collection of facts, such as numbers, word
measurements, observations, quantities etc.
Types of Data
● Qualitative data- it is a form of descriptive data.
Example- She can write fast, He is tall.
● Quantitative data- it is in the form of numerical information.
Example- An elephant has four legs.

Types of quantitative data
● Discrete data- it has a ﬁxed value that can
be counted
● Continuous data- it has no ﬁxed value but
has a range that can be measured.
Collecting & Summarizing Data
Data:
A collection of observations, facts about an object is known as Data.
Data can be in numbers or in statement/descriptive form.

Description of Data
There are various ways to describe the data:
Mode:
Mode is the value that occurs very often in the list. It can be said that
there is no mode value if no number is repeated in the list.

Median:
Median is the middle value of the list. Median divides the list into
two halves
Mean:
A mean is an average of all the numbers in the list. It can be calculated by
adding up all the numbers and then dividing the sum by the number of
values in the list.

Types of Statistics
Being a broad term, there exist different models of statistics:
Mean:
A mean is an average of two or more numerals. Mean can be computed
using Mathematical mean or Geometric mean. The mathematical mean
shows how well the commodity performs over the period whereas the
geometric mean shows the result of the investment of the same
commodity over the same period.
Regression Analysis:
It is a statistical process that determines the relationship between
variables. It is the process of understanding how the value of a
dependent variable changes when any of the independent variables is
changed.

kewness:
Skewness is the measure of the distortion from the standard distribution in
a set of data. A curve is said to be skewed if it is shifted to the left or to the
right. If the curve is extended towards the right side, it is known as the
positive skewed and if the curve is extended towards the left side, it is known
as the left-skewed.
Kurtosis:
Kurtosis is the measure of the tailedness in the frequency distribution. Data
set may have heavy-tails or light-tails.
Variance:
Variance in statistics is the measure of the data span. It is used to compare
the performances of stocks over a period of time.

Representation of Data in Statistics
There are various ways to represent data. For example- graphs, charts and
tables. The general representation of statistical data is done with the help
of:
● Bar Graph
● Pie Chart
● Line Graph
● Pictograph
● Histogram
● Frequency Distribution
● Venn Diagrams

Bar Graph:
It is the rectangular bar representation of data. The bars can be
horizontal or vertical. The length of the bar is proportional to the value
that it represents. It represents data in the form of rectangular bars
having length according to the values that they represent.

Pie Chart:
It is also known as the Circle Graph as it uses sectors of the circle to
represent the data. This graph is represented in the form of a circle which is
divided into a various number of sectors where each sector represents a
portion of the whole division.

Line Graph:
A line graph is represented by the straight line which connects the data
points. It is represented by a series of data points called markers.
Usually, a line graph is used to represent the change of the data over
the period of time.

Pictograph:
It is the representation of the frequency of data using the symbols or
pictures. A symbol can represent one or more numbers of data. It
represents data with the help of pictures.

Venn Diagrams:
It is the pictorial representation
which contains a box along with
circles. The box represents the
Sample Space and the circles
represent the events. There can be
three types of Venn diagrams:
a. Two or more than two separate
circles (When there is no
common data)
b. Overlapping Circles (When
some of the data is common)
c. Circle within a circle (When the
outer circle is the superset of
the inner circle)

Histogram:
It consists of rectangles Whose area is proportional
to the frequency of a variable and whose width is
equal to the class intervals.

Statistics XII Math Project.pdf

Statistics XII Math Project.pdf

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Statistics XII Math Project.pdf