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Statistics in Mathematics

Statistics is a branch of mathematics that deals with the analysis of data. It focuses on the organisation, interpretation, analysis, and presentation of a dataset to generate meaningful insights. In earlier classes, we start by understanding the measures of the central tendency of provided data. The three basic measures of central tendencies are – mean, median and mode. We already have an idea about these three terms, the mean measures the average of the dataset. Median represents the central value of an ordered data collection, whereas mode represents the most occurring value within the dataset.

These measures of the central tendencies of a data collection depict the gist or central characteristic of the data. These help us to interpret and analyse:

  • How is the data concentrated or dispersed from the middle point?
  • What will be the future trend of the data?
  • What is the deviation and variance of the data?
  • What precisely does the dataset represent?

Data analysis in statistics is primarily of two types:

  • Descriptive statistics: This describes the typical characteristics of the given data collection. It is the quantitative analysis of the data.
  • Inferential statistics: This mainly focuses on drawing inferences from the given data distribution. It involves the selection of models to represent data, checking the liability of the data set and so on.

Different techniques are used to find the central tendencies depending upon the type of data – grouped or ungrouped, structured or unstructured. After this, we are often required to examine the variance, which is calculated by taking the average deviation from the central point of the data whose square root determines the standard deviation of the data from the central point.

While handling data, we come across two or more random variables whose interdependency is determined by calculating the covariance, which provides information regarding the extent of dependency of one parameter on the other.

Learn about covariance in detail here.

What is Data in Statistics?

Data is a collection of facts which are analysed to draw out resourceful information. There are mainly two types of data that we work on:

  • Discrete data
  • Continuous data

Discrete data is something which has a fixed distinct data set. Let us understand this with an example; we are collecting data regarding how four-wheelers are being parked in a parking lot of an office throughout the week.

Days of weekNumber of four-wheelers parked

In this data collection, we observe that there is a particular fixed number of four-wheelers against each day of the week. The value does not vary over a range.

In contrast, continuous data does not have fixed data points but have a range of values. For example, the following data represents the height of students of standard IX.

Height of students (in cm)Number of students
90 – 1205
120 – 15038
150 – 18019
180 – 1102

Clearly, this dataset represents a set of data points which varies across a range.

To sum up, we can say that discrete data can be counted, whereas continuous data can be measured.

Learn more about the continuous variable here. 

What is Data Representation?

In statistics, we also need to represent data graphically using various methods of graphical representation of data.

  • Bar graphs
  • Line graphs
  • Histograms
  • Pie charts
  • Frequency distribution

These are some common graphical methods of representing data to interpret necessary conclusions.

Dispersion and Skewness of Data

These terms are related to the characteristics of the given data collection. Dispersion represents the extent of scattering of the data points, and skewness measures the asymmetry in the probability distribution.

Dispersion could be measured by:

  • Variance
  • Range
  • Standard deviation
  • Quartile deviation
  • Mean deviation

All of these measure how much the data is spread around the central point.

Application of Statistics

Statistics is such a branch of mathematics that has a substantial real-life application, and wherever we are dealing with any sort of data collection, we require concepts of statistics to analyse that data. Some of the common extensive applications of mathematical statistics are:

  • Scientific calculations and optimisation
  • In machine learning and artificial intelligence
  • Weather forecasting
  • Meteorology
  • Data mining, etc.
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