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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.
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.

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 What does the figure depict?

• the figure does not represent the given raw data
• the figure provides the tally and table form of the given raw data
• the figure provides the tally and table form of the given raw data

The answer is "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?

• No, the tally and table form is NOT for data with decimal values
• Yes, the data can be grouped together and tally and table form can be provided.
• Yes, the data can be grouped together and tally and table form can be provided.

The answer is "Yes, 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 95cm? 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. 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

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.

How can this continuous scale be reflected in a bar-graph?

• Make the bars touching each other to reflect continuity
• Make the bars touching each other to reflect continuity
• No. Continuous data cannot be presented in Bar-graphs

The answer is "Make the bars touching each other to reflect continuity"

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

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

Which of the following is a meaning for the word "histogram"?

• study of past events and human affairs
• written or recorded information in the form of vertical bars
• written or recorded information in the form of vertical bars

The answer is "written or recorded information in the form of vertical bars".

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

What is the term used to refer "written or recorded information in the form of vertical bars"?

• Pronunciation : Say the answer once
Spelling: Write the answer once

The answer is "histogram".

Histrogram : 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. A different grouping is presented in the figure.

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

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