# Math՚s: Data: Statistics and Statistical Data, Collection and Presentation of Data (For CBSE, ICSE, IAS, NET, NRA 2022)

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## Statistics and Statistical Data

- Statistics is the branch of mathematics that deals with the collection, organisation, analysis and interpretation of the numerical data.
- Data is a collection of facts and figures to be used for specific analysis. For Ex- Data on the number of people infected with COVID 19 in a state.

## Collection of Data

In any field of investigation, the first step is to collect the data. It is these data that will be analyzed by the investigator or the statistician to draw inferences.

**Data are of two types-**

**Primary Data-**Primary Data is collected the investigator himself from its source of origin. Some examples of primary data are: voters՚ lists, data collected in census-questionnaire etc.**Secondary Data-**Secondary Data are data collected by other governmental or private agency in the form of published reports. They are only used by the investigator for his present study.

Example (i) Anwar wanted to know the size of shoes worn by the maximum number of persons in a locality. So, he goes to each and every house and notes down the information on a sheet. Which type of data is collected here?

Answer- Since the data is firsthand which is originally collected by the investigator (Anwar) himself, it is primary data.

Example (ii) To find the number of absentees in each day of each class from to , Rishabh collects the information from the school records. The data collected here is of which type?

Answer- Since the data collected by Rishabh is not from the source of origin but from other source (school records) , this is secondary data.

## Presentation of Data

The data collected from the respondents “as it is” is called raw data. Raw data cannot be directly used for the analysis as it is not arranged. The raw data arranged in ascending or descending order is called “arrayed data” or simply “array” .

The process of arrangement of data in array, tables, graph or chart etc. so that conclusions can be drawn from it is known as PRESENTATION OF DATA.

Before we discuss the tools of data presentation, let us understand some of the basic terms associated with the presentation of data-

**Observation-**Each term in a data series is known as an observation. Ex- . Here, is an observation. Similarly, are also observations.**Frequency-**The number of times an observation occurs in a data series is known as its frequency. For Ex- The frequency of in the above series is .**Discrete Data-**Discrete Data can take only take certain values Ex- the number of rooms in a house**Continuous Data-**Continuous data can take any value within a range. Ex- Height of students in a class.

## Data Presentation Tools

**Frequency Distribution-**Frequency distribution is a table that shows the observations or classes along with their respective frequencies.- When the discrete data are arranged with frequencies, they are said known as ungrouped frequency distribution table.
- When the continuous data are divided into groups/classes, they are called grouped data.

**Bar Graph-**A bar graph is a graphical representation of the categorical data by a number of bars (rectangles) of uniform width, erected horizontally or vertically with equal space between them.**Histogram-**A histogram is a graphical representation of a grouped frequency distribution with continuous classes in the form rectangular bars with the height of each bar proportional to the frequency.**Frequency Polygon-**A frequency polygon is similar to histogram. It uses line graph instead of rectangular bars to represent frequency distribution.