Data Handling Class 6 NCERT Complete Guide

What is Data and Why Do We Organise It?

Data is a collection of numbers, measurements, words, or facts gathered to convey meaningful information. When we collect information directly from a source, it is called raw data. For example, if you write down the shoe sizes of 15 of your classmates as '5, 6, 5, 7, 5, 6, 8, 5, 7, 6, 5, 6, 7, 5, 6', it looks messy. You cannot quickly tell which shoe size is the most common. To make this raw data useful, we must organise it.

The simplest way to organize raw data is by using a table with tally marks. Tally marks are vertical lines drawn in groups of five. The first four values are represented by vertical lines (||||), and the fifth value is shown by drawing a diagonal line across the first four (<s>||||</s>). This grouping makes counting large sets of numbers fast and error-free.

How to Record and Organise Data Using Tally Marks

1. Identify Unique Categories — List down all the unique items, categories, or numbers from your raw data in the first column of your frequency distribution table.
2. Record Tally Marks — Go through your raw data list one by one. For each item you read, put a single vertical stroke (|) in the 'Tally Marks' column next to that category.
3. Group by Fives — When you reach the fifth count for any item, draw a diagonal slash across the four existing tallies to complete a block of five. This represents a bundle of 5 items.
4. Write the Frequency — Count the tally marks for each category (each bundled group counts as 5, then add any remaining single strokes) and write this number in the final 'Frequency' column.

Visual Representation: Pictographs and Bar Graphs

• Pictograph Definition: A pictograph represents data through pictures of objects. It helps answer questions on the data at a single glance. Every pictograph must have a 'Key' indicating what one picture represents (e.g., 1 flower symbol = 10 flowers).
• Example of Pictograph Reading: Suppose a pictograph has 4 smiley face symbols representing students who prefer apples. If the key says '1 smiley face = 5 students', then the total number of students who prefer apples is calculated by multiplying 4 by 5, which equals 20 students.
• Bar Graph Definition: A bar graph is a visual representation of data using horizontal or vertical bars of equal width. The lengths of these bars are proportional to the values they represent. The spacing between bars remains uniform.
• Choosing a Bar Graph Scale: If we have to represent large numbers like 100, 250, and 400 on a graph, we cannot draw 400 lines. We choose a scale such as '1 unit length = 50 units'. Thus, the bar heights will be 2 units, 5 units, and 8 units respectively, making it simple to draw.

Pro Exam Tips to Avoid Common Mistakes

• Don't Forget the Key: When drawing a pictograph, always write down your key. Without a key (e.g., 1 star = 10 marks), your diagram cannot be interpreted, and you will lose marks.
• Counting Tally Slashes: Remember that the diagonal line is the fifth stroke. Do not draw five vertical lines and then a diagonal strike, as that represents 6, not 5.
• Label the Axes: In bar graphs, always label both the horizontal axis (X-axis) and the vertical axis (Y-axis) with what they represent (like 'Years' or 'Number of Students').
• Uniform Bar Widths: Keep the width of all bars exactly equal and leave equal gaps between them to ensure your graph is mathematically accurate.

Practice Questions with Solutions

• Q: In a class test, the marks obtained by 10 students out of 10 are: 6, 7, 5, 6, 8, 5, 7, 6, 6, 9. Organise this data using tally marks and find how many students scored 6 marks. A: Step 1: List the unique marks from lowest to highest: 5, 6, 7, 8, 9. Step 2: Draw a table with three columns: Marks, Tally Marks, and Number of Students. Step 3: Count the occurrences of each mark. - Mark 5 appears 2 times (||) - Mark 6 appears 4 times (||||) - Mark 7 appears 2 times (||) - Mark 8 appears 1 time (|) - Mark 9 appears 1 time (|) Step 4: Read the frequency for mark 6. Final answer: 4 students scored 6 marks.
• Q: A pictograph shows symbols of light bulbs representing the weekly sales of an electrical shop. The key says: 1 bulb symbol = 8 bulb sales. If there are 6 full bulb symbols next to 'Wednesday', how many bulbs were sold on Wednesday? A: Step 1: Identify the number of symbols for Wednesday, which is 6. Step 2: Identify the scale value from the key, which is 1 symbol = 8 bulbs. Step 3: Multiply the number of symbols by the value of one symbol: 6 * 8 = 48. Final answer: 48 bulbs were sold on Wednesday.
• Q: In a bar graph, 1 unit length represents 10 bags of wheat. If the bar representing the year 2021 has a length of 7.5 units, how many wheat bags were sold in 2021? A: Step 1: Identify the scale: 1 unit length = 10 wheat bags. Step 2: Read the bar length for the year 2021, which is 7.5 units. Step 3: Multiply the bar length by the scale value: 7.5 * 10 = 75. Final answer: 75 wheat bags were sold in 2021.
• Q: The number of bicycles sold by a shop over four days is: Monday: 15, Tuesday: 25, Wednesday: 20, Thursday: 10. If we want to draw a bar graph, what is the best scale to use if we want the tallest bar to be 5 units high? A: Step 1: Identify the maximum value in the data set, which is 25 (sold on Tuesday). Step 2: We want the bar representing this maximum value to have a height of 5 units on our graph. Step 3: Calculate the scale by dividing the maximum value by the desired unit height: 25 / 5 = 5. Step 4: Therefore, 1 unit length on the graph must represent 5 bicycles. Final answer: The best scale is 1 unit length = 5 bicycles.

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