Information:

To know about something is known as information.

Observation:

Any recording information (Numeric or Non-Numeric) is known as observation.

Data:

Data can be defined as;

A collection of facts or information from which conclusions may be drawn.

Meaning of the word statistics:

The word statistics come from a Latin word “Status” which mean a “Political State”.

Originally meant that information about the size/number of populations in a given state.

Examples:

Covid patients, computer science students.

The word statistics is generally used in three meanings:

• Firstly, the word refers to;

“Numerically fact and systematically arranged”.

So in this sense the word statistics is always used in plural form.

Examples:

• Statistics of Covid patients
• Statistics of computer science students
• Statistics of Road accidents

• Secondly the word statistics is defined as;

“The procedure and techniques used to collect, process, and analyze numerical data to make inference(conclusion) to reach decisions in the uncertainty. In this sense the word statistics is used as singular.

Example:

Dupth rule word in cricket.

• Thirdly, the word statistics used;

“Numerical quantities calculated from sample observations.” The word statistics is plural when used in this sense.

Examples:

Mean, Median, Mode etc. which are calculated from sample observation.

•  =  = 978.25
•  =  = 1001

Definition of statistics:

“Statistics is a science of collecting, analyzing, and interpreting numerical data relating to aggregate of individual or units.”

“OR”

“Statistics is the study of the principals and method applied in collection, summarization and description of numerical data further it deals with the procedure of making inference(conclusion) about the characteristics of a population on the basis of a sample taken from the same population.”

ANP=5

PPP=2

PML=3

PTI=6

Statistics as a subject may be divided into two parts.

1. Descriptive Statistics
2. Inferential Statistics

Descriptive Statistics:

“Descriptive statistics deals with the concepts and methods concerned with the collection, summarization and description of numerical data.”

Main parts of descriptive statistics:

• Collection of data
• Classification of data
• Tabulation of data
• Graphical display of data

e.g: 27,25,32,31,87,28,88,38,3,

Inferential Statistics:

“inferential statistics deals with the procedure of making inference(conclusion) about the characteristics of population on the basis of sample taken from the same population. i.e.: estimation, hypothesis, testing, chis square, correlation etc.”

        Population

        Samples

Null Hypothesis= Research Hypothesis =H0 = Imran will come 2023

Alternative Hypothesis = H1 = HA = Imran will never come 2023

Or: Dollar rate = 170  🡪 our research hypothesis will be accepted or true.

       Dollar rate = 170

Alternative Hypothesis

Population:

“An aggregate of individual or unit.”

In statistical language the term population is applied to any finite or infinite collection of individual. It has displaced the older term “universe” it’s practically synonyms is “aggregate” A population is a collection of objects or about we want to know about something or draw inference.

Size of population is denoting by letter “N”.

Examples:

Assume a population of electric bulbs produced by a plant. We may want to estimate the average life of bulbs. The number of bulbs produced by plant may be finite or infinite.

Finite Population:

If the number of objects or units is countable in population.

e.g.: The number of houses in a city/village.

Infinite Population:

If the number of objects or units in the population is uncountable.

e.g.: The number of stars in a Galaxy.

e.g.: The number of people in universe.

Sample:

A representative which we select from a population.

Or:  a subset of the population, which represent the entire population is known as sample.

• Sample is denoted as “S” and its size is denoted by “n”.

Parameter:

The numerical value such as mean, variance and standard deviation etc. describing a characteristics of a population is known as parameters.

Or: unknown quantities, which may be vary over different sets of values forming population is called parameter. Any function of population values of a sample variable is called a parameter which is denoted by Greek letter µ, S2, S.

Statistic:

The numerical value such as mean, variance and standard deviation etc. describing a characteristic of a sample is known as statistic.

Any summary value calculated from sample of observation usually but not necessary as estimator of some population parameter is called statistic which is denoted by , S2, S. 

Sampling:

The process of selecting a sample from a population. i.e.: the sample selected has the characteristic of a whole population is known as sampling.

e.g.: the teacher, judge, the performance of a student by just asking a few questions.

• Sampling are of two types.

1. Sampling With Replacement
2. Sampling Without Replacement

1. Sampling With Replacement: If the sample unit selected is returned to the population before drawing the next sampling unit than sampling is said to be SWR.

Main Points Of SWR:

🡺 Sampling unit can be selected more than once

🡺 Population will be considering infinite.

🡺 The sampling unit will be independent.

🡺 No of samples of size “n” that could be draw with replacement from a population     of size “N” will be equal to “Nn”.

2. Sampling Without Replacement: If the sample unit selected is not returned to the population before drawing the next sampling unit than sampling is said to be SWOR.

Main Points Of SWOR:

🡺 Finite

🡺 Dependent

🡺 Only one

🡺 Size  NCn .

Sampling  With Replacement  🡺 S.W.R 🡺 Infinite

Sampling Without Replacement 🡺 S.Without.R 🡺 Finite

        N = 6

        n = 2

        (6)2 = 36 🡪 SWR

 🡺 SWOR

nCr = Combination                                 nPr = Permutation

Types Of Data By Sources:

there are two types of data.

1. Primary data
2. Secondary data

1. Primary data: the data that have been originally collected and have not underground any sort of statistical tools or treatment is called primary data. In other words, the fresh data is called primary data which is also called first-hand information collected for a certain purpose.

Methods Of Primary Data Collection:

• Email
• Questionnaire
• Direct Investigation
• Indirect Investigation
• Registration

2. Secondary data: the data that have been underground any sort of statistical tools or treatment by statistical methods, at least once. i.e.: the data have been collected, classified, tabulated or presented in some form for a certain purpose is known as secondary data.

Methods Of Secondary Data Collection:

• Official (Government) source
• SEMI Government
• Pakistan Bureau Of Statistics
• International Publication
• Bank
• Publication Of Research Organization

Types Of Data By Nature:

Types of data by nature may be divided into two types.

1. Quantitative Data
2. Qualitative Data

1. Quantitative Data: data collected by quantitative variable.

e.g. No of deaths or accident, weight, height etc.

Types:

1. Discrete Data: data collected by discrete variable called discrete data.

          e.g. Family size, No of apples in a basket etc.

     2. Continuous Data: data collected by continuous variable is called continuous data.

           e.g. Temp, Speed of a car etc.

2. Qualitative Data: data collected by qualitative variables is called qualitative data.

e.g. Education level, Religions, colors etc.