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Thought-Process to Discover Knowledge

Welcome to nubtrek.

Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.continue
mathsStatistics and ProbabilityStatistics: Grouped Data

Introduction to Grouped Data

Grouped data is introduced and explained with some examples.



click on the content to continue..

We studied about data recording and presentation with tally marks and tabular form. Then we studied about bar-graphs to represent the data in a spatially laid-out form which helps to compare data or find the minimum or maximum, etc.

tally table representation Consider the number of pens a student carries in a group of `20` students. The raw data is given as :

   `2`, `1`, `2`, `4`, `2`
   `3`, `2`, `2`, `2`, `3`
   `3`, `2`, `2`, `3`, `2`
   `2`, `2`, `4`, `2`, `2`

The figure provides the tally and tabular representation of the given raw data.

Consider the data height of students in a class of `20` students.

   `90.2`, `97.4`, `99.7`, `88.3`, `90.7`

   `93.5`, `96.8`, `89.5`, `99.5`, `98.9`

   `91.2`, `101.3`, `94.0`, `93.4`, `93.1`

   `94.7`, `96.9`, `92.8`, `91.8`, `99.6`

Note that none of the data values repeat, and there are `20` distinct values. If we are to prepare tally form of the data, each data point would get one bar.
Can the data be presented in tally and table form?

The data can be grouped together and tally and table form can be provided.

Considering the data: height of students in a class of `20` students.

   `90.2`, `97.4`, `99.7`, `88.3`, `90.7`

   `93.5`, `96.8`, `89.5`, `95.5`, `94.9`

   `91.2`, `101.3`, `94.0`, `93.4`, `93.1`

   `94.7`, `96.9`, `92.8`, `91.8`, `99.6`

The data will not be used to answer questions like "How many students are of the height `95`cm? The answer to this kind of questions is always none.

The data is primarily used to answer questions similar to

How many students are in the range `90` to `95` cm height? (which is as per the normal height for the age.)

How many students are below the lower limit `90` cm? (Which is below the healthy height for the age.)

How many students are above `100` cm ?

To cater to this, the data can be grouped into small segments of the data values. grouping of data in tabular form The figure illustrates the tally and table form of grouped data. The data is grouped as

   less than `90`

   `90` to `95`

   `95` to `100`

   above `100`

grouping of data in tabular form Considering the data: height of students in a class of `20` students.

Bar-graph are usually defined for distinct values: eg: `2`, `3`, etc.

The data in figure is continuous ranges : eg `90` to `95` and `95` to `100`, etc.

This continuous scale be reflected in a bar-graph, by making the bars touching each other to reflect continuity.

Considering the data: height of students in a class of `20` students. histogram of the continuous data. The bar graph with continuous range is shown in the figure.

This form of bar-graph is called "histogram".

The word "histogram", means written or recorded information in the form of vertical bars".

"-gram" : written or recorded information + "histo" : in the form of vertical bars.

familiarize with the terminology
histogram

Histrogram : histogram of the continuous data. A representation of data similar to bar-graph with continuous scale on the horizontal axis.

Considering the data height of students in a class of `20` students. grouping of data in tabular form A different grouping is presented in the figure.

Considering the data height of students in a class of `20` students. histogram of continuous data Histogram of the same is given in the figure.

                            
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