Here, we provided to Statistics Note By Dips Academy. Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional, to begin with, a statistical population or a statistical model to be studied.

Populations can be diverse groups of people or objects such as “all people living in a country” or “every atom composing a crystal”. Statistics deals with every aspect of data, including the planning of data collection in terms of the design of surveys and experiments. See the glossary of probability and statistics. Free download PDF Statistics Note By Dips Academy.

When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample to the population as a whole. An experimental study involves taking measurements of the system under study, manipulating the system, and then taking additional measurements using the same procedure to determine if the manipulation has modified the values of the measurements. In contrast, an observational study does not involve experimental manipulation. Free download PDF Statistics Note By Dips Academy.

Two main statistical methods are used in data analysis: descriptive statistics, which summarize data from a sample using indexes such as the mean or standard deviation, and inferential statistics, which draw conclusions from data that are subject to random variation (e.g., observational errors, sampling variation). Free download PDF Statistics Note By Dips Academy.

Descriptive statistics are most often concerned with two sets of properties of a distribution (sample or population): central tendency (or location) seeks to characterize the distribution’s central or typical value, while dispersion (or variability) characterizes the extent to which members of the distribution depart from its center and each other. Inferences on mathematical statistics are made under the framework of probability theory, which deals with the analysis of random phenomena. Free download PDF Statistics Note By Dips Academy.

A standard statistical procedure involves the collection of data leading to a test of the relationship between two statistical data sets, or a data set and synthetic data drawn from an idealized model. A hypothesis is proposed for the statistical relationship between the two data sets, and this is compared as an alternative to an idealized null hypothesis of no relationship between two data sets. Rejecting or disproving the null hypothesis is done using statistical tests that quantify the sense in which the null can be proven false, given the data that are used in the test. Free download PDF Statistics Note By Dips Academy.

Working from a null hypothesis, two basic forms of error are recognized: Type I errors (null hypothesis is falsely rejected giving a “false positive”) and Type II errors (null hypothesis fails to be rejected and an actual relationship between populations is missed giving a “false negative”). Multiple problems have come to be associated with this framework: ranging from obtaining a sufficient sample size to specifying an adequate null hypothesis.[citation needed] Free download PDF Statistics Note By Dips Academy.

Measurement processes that generate statistical data are also subject to error. Many of these errors are classified as random (noise) or systematic (bias), but other types of errors (e.g., blunder, such as when an analyst reports incorrect units) can also occur. The presence of missing data or censoring may result in biased estimates and specific techniques have been developed to address these problems. Free download PDF Statistics Note By Dips Academy.

**What Are Statistics?**

Statistics is a form of mathematical analysis that uses quantified models, representations, and synopses for a given set of experimental data or real-life studies. Statistics studies methodologies to gather, review, analyze, and draw conclusions from data. Free download PDF Statistics Note By Dips Academy.

**BOOK INFO**

**BOOK NAME** – STATISTICS NOTE

**AUTHOR** – DIPS ACADEMY

**SIZE** – 4.65MB

**PAGES** – 80

**Mathematical Statistics:**

Mathematical statistics is the application of Mathematics to Statistics, which was initially conceived as the science of the state — the collection and analysis of facts about a country: its economy, and, military, population, and so forth. Free download PDF Statistics Note By Dips Academy.

Mathematical techniques used for different analytics include mathematical analysis, linear algebra, stochastic analysis, differential equations, and measure-theoretic probability theory. Free download PDF Statistics Note By Dips Academy.

**Scope:**

Statistics is used in many sectors such as psychology, geology, sociology, weather forecasting, probability, and much more. The goal of statistics is to gain understanding from the data, it focuses on applications, and hence, it is distinctively considered as a mathematical science. Free download PDF Statistics Note By Dips Academy.

**Methods:**

The methods involve collecting, summarizing, analyzing, and interpreting variable numerical data. Here some of the methods are provided below.

- Data collection
- Data summarization
- Statistical analysis

**Data:**

Data is a collection of facts, such as numbers, words, measurements, observations, etc.

**Types of Data-**

- Qualitative data- it is descriptive data.
- Quantitative data- it is numerical information.

**Types of Statistics:**

Basically, there are two types of statistics.

- Descriptive Statistics
- Inferential Statistics

In the case of descriptive statistics, the data or collection of data is described in summary. But in the case of inferential stats, it is used to explain the descriptive one. Both these types have been used on a large scale. Free download PDF Statistics Note By Dips Academy.

There is one more type of statistics, where descriptive is transitioned into inferential stats.

**Applications:**

Some of the applications of statistic are given below:

- Applied statistics, theoretical statistics and mathematical statistics
- Machine learning and data mining
- Statistics in society
- Statistical computing
- Statistics applied to mathematics or the arts

**Statistics Examples:**

Some of the real-life examples of statistics are:

- To find the mean of the marks obtained by each student in the class whose strength is 50. The average value here is the statistics of the marks obtained.
- Suppose you need to find how many members are employed in a city. Since the city is populated with 15 lakh people, hence we will take a survey here for 1000 people (sample). Based on that, we will create the data, which is the statistic.

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