Data Handling

Objective:

This topic gives an overview of; 

  • Data Handling
  • A Pictograph
  • A bar graph
  • Double Bar Graph
  • Organising Data
  • Grouping Data
  • Bars with a difference
  • Circle Graph or Pie Chart

Data Handling

In your day-to-day life, you might have come across information, such as:

  1. Runs made by a batsman in the last 10 test matches.
  2. Number of wickets taken by a bowler in the last 10 ODIs.
  3. Marks scored by the students of your class in the Mathematics unit test.
  4. Number of story books read by each of your friends etc.

The information collected in all such cases is called data. Data is usually collected in the context of a situation that we want to study. For example, a teacher may like to know the average height of students in her class. To find this, she will write the heights of all the students in her class, organise the data in a systematic manner and then interpret it accordingly.

Sometimes, data is represented graphically to give a clear idea of what it represents. Remember the different types of graphs which we have learnt in earlier classes.

A Pictograph:

Pictorial representation of data using symbols.

  1. How many apple were produced in the month of March?
  2. In which month were maximum number of apple produced?

A bar graph:

A display of information using bars of uniform width, their heights being proportional to the respective values.

  1. What is the information given by the bar graph?
  2. In which year is the increase in the number of mark maximum?
  3. In which year is the number of mark maximum?

Double Bar Graph:

A bar graph showing two sets of data simultaneously. It is useful for the comparison of the data.

  1. What is the information given by the double bar graph?
  2. In which students has the performance improved the most?
  3. In which students has the performance deteriorated?
  4. In which students is the performance at par?

Organising Data

Usually, data available to us is in an unorganised form called raw data. To draw meaningful inferences, we need to organise the data systematically. For example, a group of students was asked for their favourite subject. The results were as listed below:

Art, Mathematics, Science, English, Mathematics, Art, English, Mathematics, English, Art, Science, Art, Science, Science, Mathematics, Art, English, Art, Science, Mathematics, Science, Art.

Which is the most liked subject and the one least liked?

The number of tallies before each subject gives the number of students who like that particular subject.This is known as the frequency of that subject.

Frequency gives the number of times that a particular entry occurs. 

From Table, Frequency of students who like English is 4. Frequency of students who like Mathematics is 5

The table made is known as frequency distribution table as it gives the number of times an entry occurs.

Grouping Data

The data regarding choice of subjects showed the occurrence of each of the entries several times. For example, Art is liked by 7 students, Mathematics is liked by 5 students and so on. This information can be displayed graphically using a pictograph or a bargraph. Sometimes, however, we have to deal with a large data. For example, consider the following marks (out of 50) obtained in Mathematics by 60 students of Class VIII: 

21, 10, 30, 22, 33, 5, 37, 12, 25, 42, 15, 39, 26, 32, 18, 27, 28, 19, 29, 35, 31, 24, 36, 18, 20, 38, 22, 44, 16, 24, 10, 27, 39, 28, 49, 29, 32, 23, 31, 21, 34, 22, 23, 36, 24, 36, 33, 47, 48, 50, 39, 20, 7, 16, 36, 45, 47, 30, 22, 17.

If we make a frequency distribution table for each observation, then the table would be too long, so, for convenience, we make groups of observations say, 0-10, 10-20 and so on, and obtain a frequency distribution of the number of observations falling in each group. Thus, the frequency distribution table for the above data can be.

Data presented in this manner is said to be grouped and the distribution obtained is called grouped frequency distribution. It helps us to draw meaningful inferences like –

  1.  Most of the students have scored between 20 and 40.
  2. Eight students have scored more than 40 marks out of 50 and so on.

Each of the groups 0-10, 10-20, 20-30, etc., is called a Class Interval (or briefly a class).

Observe that 10 occurs in both the classes, i.e., 0-10 as well as 10-20. Similarly, 20 occurs in classes 10-20 and 20-30. But it is not possible that an observation (say 10 or 20) can belong simultaneously to two classes. To avoid this, we adopt the convention that the common observation will belong to the higher class, i.e., 10 belongs to the class interval 10-20 (and not to 0-10). Similarly, 20 belongs to 20-30 (and not to 10-20). In the class interval, 10-20, 10 is called the lower class limit and 20 is called the upper class limit. Similarly, in the class interval 20-30, 20 is the lower class limit and 30 is the upper class limit. Observe that the difference between the upper class limit and lower class limit for each of the class intervals 0-10, 10-20, 20-30 etc., is equal, (10 in this case). This difference between the upper class limit and lower class limit is called the width or size of the class interval.

Bars with a difference

Let us again consider the grouped frequency distribution of the marks obtained by 60 students in Mathematics test.

This is displayed graphically as in the adjoining graph.Observe that, here we have represented the groups of observations (i.e., class intervals)on the horizontal axis.

The height of the bars show the frequency of the class-interval. Also, there is no gap between the bars as there is no gap between the class-intervals. The graphical representation of data in this manner is called a histogram. The following graph is another histogram.

From the bars of this histogram, we can answer the following questions:

  1. How many teachers are of age 45 years or more but less than 50 years?
  2. How many teachers are of age less than 35 years?

Circle Graph or Pie Chart

These are called circle graphs. A circle graph shows the relationship between a whole and its parts. Here, the whole circle is divided into sectors. The size of each sector is proportional to the activity or information it represents.

For example, in the above graph, the proportion of the sector for hours spent in sleeping

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»=«/mo»«mfrac»«mrow»«mi»n«/mi»«mi»u«/mi»«mi»m«/mi»«mi»b«/mi»«mi»e«/mi»«mi»r«/mi»«mo»§nbsp;«/mo»«mi»o«/mi»«mi»f«/mi»«mo»§nbsp;«/mo»«mi»s«/mi»«mi»l«/mi»«mi»e«/mi»«mi»e«/mi»«mi»p«/mi»«mi»i«/mi»«mi»n«/mi»«mi»g«/mi»«mo»§nbsp;«/mo»«mi»h«/mi»«mi»o«/mi»«mi»u«/mi»«mi»r«/mi»«mi»s«/mi»«/mrow»«mrow»«mi»w«/mi»«mi»h«/mi»«mi»o«/mi»«mi»l«/mi»«mi»e«/mi»«mo»§nbsp;«/mo»«mi»d«/mi»«mi»a«/mi»«mi»y«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mn»8«/mn»«mo»§nbsp;«/mo»«mi»h«/mi»«mi»o«/mi»«mi»u«/mi»«mi»r«/mi»«mi»s«/mi»«/mrow»«mrow»«mn»24«/mn»«mo»§nbsp;«/mo»«mi»h«/mi»«mi»o«/mi»«mi»u«/mi»«mi»r«/mi»«mi»s«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mn»1«/mn»«mn»3«/mn»«/mfrac»«/math»

So, this sector is drawn as «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mn»3«/mn»«/mfrac»«/math» part of the circle. Similarly, the proportion of the sector for hours spent in school

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»=«/mo»«mfrac»«mrow»«mi»n«/mi»«mi»u«/mi»«mi»m«/mi»«mi»b«/mi»«mi»e«/mi»«mi»r«/mi»«mo»§nbsp;«/mo»«mi»o«/mi»«mi»f«/mi»«mo»§nbsp;«/mo»«mi»s«/mi»«mi»c«/mi»«mi»h«/mi»«mi»o«/mi»«mi»o«/mi»«mi»l«/mi»«mo»§nbsp;«/mo»«mi»h«/mi»«mi»o«/mi»«mi»u«/mi»«mi»r«/mi»«mi»s«/mi»«/mrow»«mrow»«mi»w«/mi»«mi»h«/mi»«mi»o«/mi»«mi»l«/mi»«mi»e«/mi»«mo»§nbsp;«/mo»«mi»d«/mi»«mi»a«/mi»«mi»y«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mn»6«/mn»«mo»§nbsp;«/mo»«mi»h«/mi»«mi»o«/mi»«mi»u«/mi»«mi»r«/mi»«mi»s«/mi»«/mrow»«mrow»«mn»24«/mn»«mo»§nbsp;«/mo»«mi»h«/mi»«mi»o«/mi»«mi»u«/mi»«mi»r«/mi»«mi»s«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mn»1«/mn»«mn»4«/mn»«/mfrac»«/math»

So this sector is drawn «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mn»4«/mn»«/mfrac»«/math»of the circle. Similarly, the size of other sectors can be found. Add up the fractions for all the activities.A circle graph is also called a pie chart.

Drawing pie charts

The favourite flavours of ice-creams for students of a school is given in percentages as follows.

Flavours Percentage of students
Preferring the flavours
Chocolate 50%
Vanilla 25%
Other flavours 50%

Let us represent this data in a pie chart. The total angle at the centre of a circle is 360°.The central angle of the sectors will be a fraction of 360°. We make a table to find the central angle of the sectors.

 

  • Draw a circle with any convenient radius.Mark its centre (O) and a radius (OA).  

  

  • The angle of the sector for chocolate is 180°. Use the protractor to draw ∠AOB = 180°.

 

  • Continue marking the remaining sectors.

 

Summary:

  1. Data mostly available to us in an unorganised form is called raw data.
  2. In order to draw meaningful inferences from any data, we need to organise the data systematically.
  3. Frequency gives the number of times that a particular entry occurs.
  4. Raw data can be ‘grouped’ and presented systematically through ‘grouped frequency distribution’.
  5. Grouped data can be presented using histogram.Histogram is a type of bar diagram, where the class intervals are shown on the horizontal axis and the heights of the bars show the frequency of the class interval. Also, there is no gap between the bars as there is no gap between the class intervals.
  6. Data can also presented using circle graph or pie chart.A circle graph shows the relationship between a whole and its part.

 

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