Data is a collection of observations. Visual representation of data will help us to understand it better and remember the facts easily. The word ‘data’ means collection of information in the form of numerical figures, or a set of given facts.
• The marks obtained by 10 students of a class in a test are:
• 76, 83, 95, 100, 56, 32, 80, 67, 75, 46
• The following table gives the data regarding the favourite game of 100 students of a school:
| Number of Students
When some information is collected and presented randomly, then it is called raw data. A data classified into groups is called grouped data.
The raw data can be arranged in following ways.
1) Alphabetical or serial order
2) Ascending order
3) Descending order
Frequency of the observation
The number of times an observation occurs in the given data, is called the frequency of the observation.
Frequency distributions are two types. i) Discreate frequency distribution ii) Continuous or grouped frequency distribution.
Steps of discreate frequency distribution
Steps of Continuous or grouped frequency distribution
- Obtain the given raw data.
- Prepare a table with three columns, first for variable under study such as marks, weight, height, etc., second for 'Tally marks' and third for the total, representing corresponding frquency to each value or size of the variable.
- Place all the values of the variable in the first column in ascending order.
- Take the first observation in the raw data and put a bar in the second column opposite to it. Then take the second observation in the given raw data and put a bar opposite to it. Continue this process till all the observations in the given raw data are exhausted. For the sake of convenience, record tally marks in bunches of five, the fifth is obtained by crossing diagonally the other four. Leave some space between each block of bars.
- Count the number of bars (tally marks) in respect of each value of the variable and place it in the third column.
- Give a suitable tittle to the frequency distribution table so that it conveys exactly what the table is about.
- Determine the maximum and minimum value of the variable occurring in the data.
- Decide upon the number of classes to be formed. Note that the number of classes should be in range of 5 to 15.
- Find the difference between the maximum value and minimum and divide this difference by the number of classes to be formed to determine the class interval. The difference between the maximum value and minimum value in a data is called range.
- Be sure that there must be classes with us to include minimum and maximum occurring in the data.
- Take each item from the data, one at a time and put a tally mark (|) against the class to which the item belongs . If tally marks are more than 4, then record them in the bunches of five, the fifth one is marked by crossing diagonally the first four.
- By counting determine the total number of tally marks in each class, which gives us the frequency of the class.
- Check that the total of all frequencies is same as the total number of observations.
- Give a suitable title to the frequency table so that it conveys exactly what the table is about.
Data in raw form can be represented in the form of pictures and diagrams. It makes the given data attractive to the observer. Also, it is easy to understand and to compare it with other information.
Some commonly used diagrams to represent numerical data are:
• Bar graph
• Double bar graph
• Pie-diagrams or Pie-charts
Pictographs represent data through appropriate pictures. In pictographs, the same type of symbol or picture is used to represent the data. Each symbol is used to represent a certain value, and this is mentioned clearly in the graph.
For example, one symbol may represent 25 students.
The following pictograph represents the number of students coming to a college by different means of transport:
A representation of data with the help of bars or rectangles in a diagram is called a bar graph or a bar diagram.
Here, each bar represents only one value of the data, and hence, there are as many bars as the number of values in the data. The length or height of a bar indicates the value of the item. The width of a bar and the gap between the bars is kept uniform to make the diagram look neat.
The following bar graph represents the production of rice in different years:
Sometimes, organising data becomes a tedious process. In such cases, we group the raw data. We write the groups as intervals. Each group is called a class interval. The class interval will have a lower class limit and an upper class limit.
The difference between the upper class limit and the lower class limit is called the width or size of the class interval. The number of times a particular item appears within a particular class interval is called frequency. The span of a class interval is called the width or size of the class interval.
Double bar graph:
A graph showing two sets of data simultaneously is called a double bar graph. It is useful for comparing two sets of data.
The following graph shows the strength of boys and girls in a school in different years:
A pie diagram or a pie chart is a circle divided into several sectors. The circle represents the total value of the given data, and the sectors represent the proportion of the components of the total. It is also called an angular diagram or a circular diagram.
Central angle of a component = (Value of the component / Sum of the component values) × 360° .
The monthly expenditure on various items of a family is given below:
|| House Rent.
|| School Fees
| Amount Spent
|| Rs. 2500
|| Rs. 2700
|| Rs. 2400
|| Rs. 1400
Its representation in a pie diagram is as shown: