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May 15, 2024**Data Representation: **Data representation is a technique for analysing numerical data. The relationship between facts, ideas, information, and concepts is depicted in a diagram via data representation. It is a fundamental learning strategy that is simple and easy to understand. It is always determined by the data type in a specific domain. Graphical representations are available in many different shapes and sizes.

In mathematics, a graph is a chart in which statistical data is represented by curves or lines drawn across the coordinate point indicated on its surface. It aids in the investigation of a relationship between two variables by allowing one to evaluate the change in one variable’s amount in relation to another over time. It is useful for analysing series and frequency distributions in a given context. On this page, we will go through two different types of graphs that can be used to graphically display data. Continue reading to learn more.

**Definition: **After collecting the data, the investigator has to condense them in tabular form to study their salient features. Such an arrangement is known as the presentation of data.

Any information gathered may be organised in a frequency distribution table, and then shown using pictographs or bar graphs. A bar graph is a representation of numbers made up of equally wide bars whose lengths are determined by the frequency and scale you choose.

The collected raw data can be placed in any one of the given ways:

- Serial order of alphabetical order
- Ascending order
- Descending order

**Example: **Let the marks obtained by \(30\) students of class VIII in a class test, out of \(50\)according to their roll numbers, be:

\(39,\,25,\,5,\,33,\,19,\,21,\,12,41,\,12,\,21,\,19,\,1,\,10,\,8,\,12\)

\(17,\,19,\,17,\,17,\,41,\,40,\,12,41,\,33,\,19,\,21,\,33,\,5,\,1,\,21\)

The data in the given form is known as raw data or ungrouped data. The above-given data can be placed in the serial order as shown below:

Now, for say you want to analyse the standard of achievement of the students. If you arrange them in ascending or descending order, it will give you a better picture.

**Ascending order:**

\(1,\,1,\,5,\,5,\,8,\,10,\,12,12,\,12,\,12,\,17,\,17,\,17,\,19,\,19\)

\(19,\,19,\,21,\,21,\,21,\,25,\,33,33,\,33,\,39,\,40,\,41,\,41,\,41\)

**Descending order:**

\(41,\,41,\,41,\,40,\,39,\,33,\,33,33,\,25,\,21,\,21,\,21,\,21,\,19,\,19\)

\(19,\,19,\,17,\,17,\,17,\,12,\,12,12,\,12,\,10,\,8,\,5,\,5,1,\,1\)

When the raw data is placed in ascending or descending order of the magnitude is known as an array or arrayed data.

A few of the graphical representation of data is given below:

- Bar chart
- Frequency distribution table
- Histogram
- Pie chart
- Line graph

The bar graph represents the qualitative data visually. The information is displayed horizontally or vertically and compares items like amounts, characteristics, times, and frequency.

The bars are arranged in order of frequency, so more critical categories are emphasised. By looking at all the bars, it is easy to tell which types in a set of data dominate the others. Bar graphs can be in many ways like single, stacked, or grouped.

A frequency table or frequency distribution is a method to present raw data in which one can easily understand the information contained in the raw data.

The frequency distribution table is constructed by using the tally marks. Tally marks are a form of a numerical system with the vertical lines used for counting. The cross line is placed over the four lines to get a total of \(5\).

**Example:**

Consider a jar containing the different colours of pieces of bread as shown below:

Construct a frequency distribution table for the data mentioned above.

**Answer:**

The histogram is another kind of graph that uses bars in its display. The histogram is used for quantitative data, and ranges of values known as classes are listed at the bottom, and the types with greater frequencies have the taller bars.

A histogram and the bar graph look very similar; however, they are different because of the data level. Bar graphs measure the frequency of the categorical data. A categorical variable has two or more categories, such as gender or hair colour.

The pie chart is used to represent the numerical proportions of a dataset. This graph involves dividing a circle into different sectors, where each of the sectors represents the proportion of a particular element as a whole. Thus, it is also known as a circle chart or circle graph.

A graph that uses points and lines to represent change over time is defined as a line graph. In other words, it is the chart that shows a line joining multiple points or a line that shows the link between the points.

The diagram illustrates the quantitative data between two changing variables with the straight line or the curve that joins a series of successive data points. Linear charts compare two variables on the vertical and the horizontal axis.

We have a few rules to present the information in the graphical representation effectively, and they are given below:

**Suitable Title:**Ensure that the appropriate title is given to the graph, indicating the presentation’s subject.**Measurement Unit:**Introduce the measurement unit in the graph.**Proper Scale:**To represent the data accurately, choose an appropriate scale.**Index:**In the Index, the appropriate colours, shades, lines, design in the graphs are given for better understanding.**Data Sources:**At the bottom of the graph, include the source of information wherever necessary.**Keep it Simple:**Build the graph in a way that everyone should understand easily.**Neat:**You have to choose the correct size, fonts, colours etc., in such a way that the graph must be a model for the presentation of the information.

**Q.1. Construct the frequency distribution table for the data on heights in \(({\rm{cm}})\) of \(20\) boys using the class intervals \(130 – 135,135 – 140\) and so on. The heights of the boys in \({\rm{cm}}\) are: **

**Ans:** The frequency distribution for the above data can be constructed as follows:

**Q.2. Write the steps of the construction of Bar graph?Ans: **To construct the bar graph, follow the given steps:

1. Take a graph paper, draw two lines perpendicular to each other, and call them horizontal and vertical.

2. You have to mark the information given in the data like days, weeks, months, years, places, etc., at uniform gaps along the horizontal axis.

3. Then you have to choose the suitable scale to decide the heights of the rectangles or the bars and then mark the sizes on the vertical axis.

4. Draw the bars or rectangles of equal width and height marked in the previous step on the horizontal axis with equal spacing.

The figure so obtained will be the bar graph representing the given numerical data.

**Q.3. Read the bar graph and then answer the given questions:I. Write the information provided by the given bar graph.II. What is the order of change of the number of students over several years?III. In which year is the increase of the student maximum?IV. State whether true or false.The enrolment during \(1996 – 97\) is double that of \(1995 – 96\) **

**Ans:**

I. The bar graph represents the number of students in class \({\rm{VI}}\) of a school during the academic years \(1995 – 96\,to\,1999 – 2000\).

II. The number of stcccccudents is changing in increasing order as the heights of bars are growing.

III. The increase in the number of students in uniform and the increase in the height of bars is uniform. Hence, in this case, the growth is not maximum in any of the years. The enrolment in the years is \(1996 – 97\, = 200\).

and the enrolment in the years is \(1995 – 96\, = 150\).

IV. The enrolment in \(1995 – 97\,\) is not double the enrolment in \(1995 – 96\). So the statement is false.

**Q.4. Write the frequency distribution for the given information of ages of \(25\) students of class VIII in a school.\(15,\,16,\,16,\,14,\,17,\,17,\,16,\,15,\,15,\,16,\,16,\,17,\,15\)\(16,\,16,\,14,\,16,\,15,\,14,\,15,\,16,\,16,\,15,\,14,\,15\)**

**Q.5. There are \(20\) students in a classroom. The teacher asked the students to talk about their favourite subjects. The results are listed below:**

**By looking at the above data, which is the most liked subject?Ans:** Representing the above data in the frequency distribution table by using tally marks as follows:

From the above table, we can see that the maximum number of students \((7)\) likes mathematics.

**Also, Check –**

In the given article, we have discussed the data representation with an example. Then we have talked about graphical representation like a bar graph, frequency table, pie chart, etc. later discussed the general rules for graphic representation. Finally, you can find solved examples along with a few FAQs. These will help you gain further clarity on this topic.

**Q.1: How is data represented?A: **The collected data can be expressed in various ways like bar graphs, pictographs, frequency tables, line graphs, pie charts and many more. It depends on the purpose of the data, and accordingly, the type of graph can be chosen.

**Q.2:** **What are the different types of data representation?****A**: The few types of data representation are given below:

1. Frequency distribution table

2. Bar graph

3. Histogram

4. Line graph

5. Pie chart

**Q.3:** **What is data representation, and why is it essential?****A:** After collecting the data, the investigator has to condense them in tabular form to study their salient features. Such an arrangement is known as the presentation of data.**Importance:** The data visualization gives us a clear understanding of what the information means by displaying it visually through maps or graphs. The data is more natural to the mind to comprehend and make it easier to rectify the trends outliners or trends within the large data sets.

**Q.4:** **What is the difference between data and representation?****A:** The term data defines the collection of specific quantitative facts in their nature like the height, number of children etc., whereas the information in the form of data after being processed, arranged and then presented in the state which gives meaning to the data is data representation.

**Q.5:** *Why do we use data representation?***A: **The data visualization gives us a clear understanding of what the information means by displaying it visually through maps or graphs. The data is more natural to the mind to comprehend and make it easier to rectify the trends outliners or trends within the large data sets.