CBSE Class 6 Maths: Data Handling Exercise 9.2 Explained

What is Data Handling and Why is it Important?

Imagine you want to know which fruit is most popular among your friends. You ask each friend, "What is your favourite fruit?" and write down their answers. This collection of raw information is called data. Data handling is the process of collecting, organizing, and presenting this data in a meaningful way so that we can draw conclusions from it.

Why is this important? Because raw data can be messy and hard to understand. For example, if 30 friends tell you their favorite fruit, just looking at a long list of names and fruits can be confusing. But if you organize it into a table and then show it in a pictograph (using pictures) or a bar graph (using bars), you can quickly see that 10 friends like apples, 8 like bananas, and so on. This makes it much easier to answer questions like "Which fruit is liked by most friends?" or "How many more friends like apples than oranges?" Data handling helps us make sense of the world around us by transforming raw facts into clear, understandable insights. In Data Handling Ex 9 2, you'll practice these essential skills to become a data detective!

Key Terms in Data Handling

Data

A collection of numerical facts or figures, or other information, gathered for a specific purpose. For example, the number of students present in class each day.

Raw Data

Data collected in its original, unorganized form, exactly as it was gathered. This data needs to be sorted and organized.

Tally Marks

A quick way of counting and recording data in groups of five. A straight vertical line ( | ) represents one unit, and the fifth unit is marked by a diagonal line across the first four ( <s>||||</s> ).

Frequency

The number of times a particular observation or item appears in a given set of data. It tells us how often something occurs.

Pictograph

A way of representing data using pictures or symbols. Each symbol represents a certain number of items, as shown in a 'key'.

Bar Graph

A visual representation of data using rectangular bars of uniform width. The length or height of each bar is proportional to the value (frequency) it represents. Bars can be drawn vertically or horizontally.

Steps to Create Pictographs and Bar Graphs

1. Step 1: Collect and Organize Data using Tally Marks — First, gather your raw data. Then, list all the different categories or observations. For each observation, use tally marks to count its frequency. This makes counting much easier and prevents errors. For example, if you are counting favorite colours, you would make a list: Red, Blue, Green, Red, Yellow, Blue... and then tally them up.
2. Step 2: Choose a Suitable Scale (for Pictographs and Bar Graphs) — Before drawing, you need to decide what each picture (for pictograph) or each unit on the axis (for bar graph) will represent. This is called the 'key' for a pictograph or 'scale' for a bar graph. If you have large numbers, one picture or one unit might represent 5, 10, or even 100 items. Choose a scale that allows your graph to fit on the page and be easy to read.
3. Step 3: Draw the Pictograph — For a pictograph, draw a suitable picture or symbol that represents your items. Create a 'key' that clearly states what one symbol stands for (e.g., '1 car = 5 vehicles'). Then, for each category, draw the number of symbols required according to its frequency and your chosen key. Remember to add a title.
4. Step 4: Draw the Bar Graph — For a bar graph, draw two axes: a horizontal axis and a vertical axis. Label them clearly (e.g., 'Days of Week' on horizontal, 'Number of Students' on vertical). Mark the scale on one axis (usually the vertical axis for frequency). Then, draw bars of uniform width for each category. The height of each bar should correspond to its frequency based on the scale. Ensure there is equal spacing between bars. Add a title to your bar graph.

Worked Examples from Data Handling Ex 9 2

• Example 1: Interpreting a Pictograph The following pictograph shows the number of cars sold by a dealer over five months. Month | Number of Cars ---|--- January | 🚗 🚗 🚗 🚗 February | 🚗 🚗 🚗 🚗 🚗 🚗 March | 🚗 🚗 🚗 April | 🚗 🚗 🚗 🚗 🚗 May | 🚗 🚗 🚗 🚗 🚗 🚗 🚗 Key: 🚗 = 10 cars (a) How many cars were sold in March? (b) In which month was the maximum number of cars sold? (c) How many more cars were sold in February than in March? Solution: (a) Cars sold in March: From the pictograph, there are 3 car symbols for March. Since each symbol represents 10 cars, total cars sold = 3 × 10 = 30 cars. (b) Maximum sales month: May has 7 car symbols (70 cars), which is the most. So, the maximum number of cars was sold in May. (c) Difference in sales (February vs. March): Cars sold in February = 6 symbols × 10 cars/symbol = 60 cars. Cars sold in March = 3 symbols × 10 cars/symbol = 30 cars. Difference = 60 - 30 = 30 cars. So, 30 more cars were sold in February than in March.
• Example 2: Creating a Bar Graph from Tally Marks The number of students in Class 6 who like different sports are given below: Sport | Tally Marks | Frequency ---|---|--- Football | <s>||||</s> | 5 Cricket | <s>||||</s> <s>||||</s> | 10 Basketball | <s>||||</s> | 5 Badminton | <s>||||</s> || | 7 Volleyball | <s>||||</s> | 5 Represent the data using a bar graph. Solution: 1. Choose a Scale: The highest frequency is 10. Let's choose a scale of 1 unit = 1 student on the vertical axis. 2. Draw Axes: Draw a horizontal axis for 'Sports' and a vertical axis for 'Number of Students'. 3. Label Axes: Label the horizontal axis with 'Sports' and mark points for Football, Cricket, Basketball, Badminton, and Volleyball. Label the vertical axis 'Number of Students' and mark units from 0 to 10. 4. Draw Bars: Draw rectangular bars of uniform width for each sport. The height of each bar will correspond to its frequency: Football: Height 5 units Cricket: Height 10 units Basketball: Height 5 units Badminton: Height 7 units Volleyball: Height 5 units 5. Add Title: Give the graph a title, e.g., 'Favourite Sports of Class 6 Students'. (Self-correction: Since I can't draw the graph here, the explanation provides the steps clearly, which is the core learning for Class 6.)*

Exam Tips for Data Handling Exercise 9.2

When you're tackling problems from Data Handling Ex 9 2 Class 6 NCERT, keep these tips in mind to score full marks:

1. Read the Question Carefully: Before you start, understand what type of graph you need to draw (pictograph or bar graph) and what information you need to extract from a given graph.
2. Tally Marks Accuracy: When counting raw data, be very careful with tally marks. A mistake here will lead to wrong frequencies and an incorrect graph. Always cross-check your tallies.
3. Choose the Right Scale: This is crucial. If numbers are small (e.g., up to 20), a scale of 1 unit = 1 item might be fine. If numbers are large (e.g., up to 100 or more), choose 1 unit = 5 or 10 items. The scale should allow the graph to be clear, not too squashed or too spread out.
4. Labels and Title: Always label both axes of your bar graph and provide a clear title. For pictographs, the 'key' explaining what each symbol represents is absolutely essential. Without these, your graph is incomplete and unclear.
5. Uniformity: For bar graphs, ensure all bars have the same width and there is equal spacing between them. For pictographs, ensure all symbols are of the same size and are neatly drawn. Your presentation matters!

Practice Questions with Solutions

• Q: The following table shows the number of books read by 5 friends in a week. Friend | Number of Books ---|--- Aryan | 4 Bhavya | 7 Chitra | 5 Danish | 3 Eva | 6 Draw a pictograph for this data, using a symbol 📖 to represent 1 book. A: Step 1: Understand the data. We have the number of books read by 5 friends. Step 2: Choose a symbol. The question specifies 📖 = 1 book. Step 3: Draw the pictograph for each friend. Aryan: 📖 📖 📖 📖 Bhavya: 📖 📖 📖 📖 📖 📖 📖 Chitra: 📖 📖 📖 📖 📖 Danish: 📖 📖 📖 Eva: 📖 📖 📖 📖 📖 📖 Step 4: Add a title: 'Books Read by Friends in a Week'. Final answer: The pictograph is drawn as shown in Step 3.
• Q: A survey of 30 students in Class 6 asked about their favourite animal. The results were: Dog, Cat, Rabbit, Dog, Dog, Cat, Fish, Rabbit, Dog, Cat, Dog, Rabbit, Fish, Dog, Cat, Dog, Rabbit, Rabbit, Cat, Dog, Fish, Dog, Cat, Dog, Rabbit, Dog, Cat, Fish, Rabbit, Dog. (a) Make a tally mark table for this data. (b) Which animal is the most popular? A: Step 1: List the unique animals and start making tally marks. Dog: | | | | | | | | | | | | | | (Count = 12) Cat: | | | | | | | | | (Count = 9) Rabbit: | | | | | | | | | (Count = 8) Fish: | | | | (Count = 4) Step 2: Create the frequency table. Animal | Tally Marks | Frequency ---|---|--- Dog | <s>||||</s> <s>||||</s> || | 12 Cat | <s>||||</s> <s>||||</s> || | 9 Rabbit | <s>||||</s> <s>||||</s> ||| | 8 Fish | <s>||||</s> ||| | 4 Step 3: Answer part (b) by looking at the frequency column. The highest frequency is 12, which corresponds to 'Dog'. Final answer: (a) The tally mark table is shown above. (b) Dog is the most popular animal.
• Q: The marks obtained by 5 students in a Math test (out of 10) are: 8, 5, 9, 8, 6. Draw a bar graph to represent this data. A: Step 1: List the data: Students and their marks. Student 1: 8, Student 2: 5, Student 3: 9, Student 4: 8, Student 5: 6. Step 2: Choose a suitable scale. Since marks are small (up to 10), we can take 1 unit = 1 mark on the vertical axis. Step 3: Draw horizontal and vertical axes. Label horizontal axis as 'Students' and vertical axis as 'Marks Obtained'. Step 4: Draw bars for each student up to their respective marks. Bar for Student 1 (Marks 8) will go up to 8 units. Bar for Student 2 (Marks 5) will go up to 5 units. Bar for Student 3 (Marks 9) will go up to 9 units. Bar for Student 4 (Marks 8) will go up to 8 units. * Bar for Student 5 (Marks 6) will go up to 6 units. Step 5: Add a title: 'Marks Obtained by Students in Math Test'. Final answer: The bar graph with clearly labelled axes and bars of respective heights is drawn.
• Q: A shopkeeper sold the following number of ice cream cones over five days: Monday: 25, Tuesday: 30, Wednesday: 15, Thursday: 40, Friday: 35. Represent this data using a pictograph. Use the symbol 🍦 to represent 5 ice cream cones. A: Step 1: Understand the data: number of cones sold per day. Step 2: Define the key: 🍦 = 5 ice cream cones. This means for every 5 cones, we draw one symbol. Step 3: Calculate the number of symbols for each day: Monday: 25 cones / 5 cones/symbol = 5 symbols Tuesday: 30 cones / 5 cones/symbol = 6 symbols Wednesday: 15 cones / 5 cones/symbol = 3 symbols Thursday: 40 cones / 5 cones/symbol = 8 symbols * Friday: 35 cones / 5 cones/symbol = 7 symbols Step 4: Draw the pictograph: Day | Number of Ice Cream Cones ---|--- Monday | 🍦 🍦 🍦 🍦 🍦 Tuesday | 🍦 🍦 🍦 🍦 🍦 🍦 Wednesday | 🍦 🍦 🍦 Thursday | 🍦 🍦 🍦 🍦 🍦 🍦 🍦 🍦 Friday | 🍦 🍦 🍦 🍦 🍦 🍦 🍦 Step 5: Add a title: 'Ice Cream Cones Sold Over Five Days'. Final answer: The pictograph is drawn as shown in Step 4, with the key and title.

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