Q.You might have observed that amount spent on petrol is directly dependent on the distance travelled by the vehicle. Here one quantity affects the another. So here quantity of petrol consumed is an independent variable and amount of petrol bill is the dependent variable. Explain how this kind of relationship between such variables can be shown through a graph.

Data Representation and Visualization – A First Look

Imagine you have a pile of numbers: the marks of 50 students in a test. If I hand you a list of 50 numbers, you can't see the story. Who did well? How many failed? Is the class strong or weak? The raw numbers are just noise.

Data representation is the act of organizing that noise into a shape you can read. Data visualization is the act of drawing that shape so your eyes can see the pattern instantly.

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The Intuition: From Pile to Picture

Think of a messy room. You can't find anything. Data representation is like sorting the clothes into piles — shirts here, socks there. Data visualization is like hanging them on labelled hooks so you see at a glance what you have.

For the test marks, the first step is representation: you group the marks into ranges (0–10, 10–20, … 90–100) and count how many students fall in each. That's a frequency distribution table. Now the noise has structure.

The second step is visualization: you draw bars whose heights match those counts. That's a histogram. Now you see at a glance: most students scored between 40 and 60, a few scored above 80, and nobody scored below 20. The story jumps out.

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The Precise Statement

Data Representation is the process of organizing raw data into a structured form — typically a table — that reveals its distribution. Common forms are:

• Ungrouped frequency distribution (list each value and its count)
• Grouped frequency distribution (values grouped into class intervals)
• Cumulative frequency distribution (running total of counts)

Data Visualization is the graphical display of that structured data, using charts that exploit the human eye's ability to spot patterns, trends, and outliers. Common forms are:

• Bar graph (for categorical data)
• Histogram (for continuous data grouped into intervals)
• Frequency polygon (line joining midpoints of histogram bars)
• Pie chart (for proportions)
• Line graph (for trends over time)

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A Concrete Example

Take these 20 marks (out of 50):

12, 35, 28, 42, 18, 35, 40, 22, 30, 45, 15, 38, 33, 27, 41, 19, 36, 29, 44, 31

Step 1 – Represent (group into intervals of 10):

Now you know: most students are in the 30–50 range, few below 20.

Step 2 – Visualize (draw a histogram):

Frequency
  6 |          ████  ████
  5 |          ████  ████
  4 |  ████  ████    ████
  3 |  ████  ████    ████
  2 |  ████  ████    ████
  1 |  ████  ████    ████
    +------------------------ …