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Standard Deviation

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When we learn the subject of statistics in our secondary classes, we study mainly the central measures of tendency and the measures of dispersion. As most of you might know, mean, median, mode, etc are various measures of central tendency. Similarly, the various measures of dispersion are range, mean deviation, standard deviation, quartile deviation, and so on. Out of the various measures of dispersion, the standard deviation is one of the most prominent measures of dispersion that is used widely by various mathematicians. In layman’s language, we can define standard deviation as the positive square root of the variance. The indicator that shows various data points about the central tendency of the mean is called standard deviation.

Statistics
Statistics is a scientific study that involves the collection of data with accurate interpretation and presentation. The accumulation of large size data into a  compact and organized numerical set can be called statistics. It can be arranged in the form of numerical tables, graphs, or charts. The statistical data of various fields and events helps in understanding them with close analysis and authentic calculation. However, the aggregation and interpretation of statistical data become a hard mountain to climb for researchers and experts. The application of statistics is universal, it is used in reviewing the demographics of the countries.

Historical Background of Statistics
There are many sources that tell us about the origin of statistics. Some suggest that statistics come from the Latin word ‘status’ and others are of the opinion that statistics either originated from the Italian word ‘Statista’ or from the German word ‘Statistik’. In the fourth century B.C, when Chandragupta was the ruler with  Kautilya or Chanakya as its administrator, the records of birth rate and death rate of the kingdom were recorded in his famous book ‘Arthashastra’. Arthashastra is one of the prominent examples of the use of statistics. Abu Fazl has mentioned statistical data based on agriculture in his book Ain-i-Akbari. Around 300 B.C to 2000 B.C, during the reign of the pharaoh of Egypt, the first census was conducted.

Types of  Statistics

Statistics can be categorized into two types which are as follows:
Descriptive statistics and Inferential statistics.

  • Descriptive Statistics: In this type of statistics, the data is presented in a precise way. The summarization of data is processed by some parameters such as mean or standard deviations. Descriptive statistics involves the use of charts, tables, and graphs for the interpretation and representation of the data. It also consists of mean, median, and mode. These statistics are created and represented in the form of tables, graphs, and charts which give detailed information like pie charts, bars, scatter plots, etc. Descriptive statistics are very formal and elaborative in nature. The elements of the collected data can be understood with the help of descriptive statistics and the base for testing hypotheses is also created by using descriptive data.

Descriptive statistics are further divided into the following kinds:

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  1. Measure frequency
  2. Measure of dispersion
  3. Measure of central tendency
  4. Measure of position

Inferential Statistics:  In this type of statistics, the descriptive statistics are further summarised and explained. Once the data is collected and analyzed, inferential statistics are needed to describe the collected data. Inferential statistics gives the advantage of giving statements that sometimes go ahead of the available statistical data. For example, the process of deriving estimates from hypothetical research.

Inferential statistics are categorized into the following types:

  1. Confidence interval
  2. T-test or ANOVA

Significance of Statistics

  • In the field of economics, business, social science, and others, statistical data provides close analysis and representation of such fields which helps to foresee problems and make
  • Statistics are useful in collecting authentic quantitative data.
  • It converts large and complex data into simple data which is understandable to all.

If you want to learn more in detail about these interesting concepts, visit Cuemath to book a free session.

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