CBSE Class 6 Maths Chapter 9: Data Handling Notes

Important Terminology

Data

A collection of numbers or facts gathered together to give some useful information.

Raw Data

The initial collection of facts or numbers that has not been sorted or organized.

Recording Data

The process of listing or noting down collected facts systematically as they occur.

Tally Marks

A quick, visual method of recording counts in groups of five, where vertical lines represent counts and a diagonal line bundles them into a set of five.

Pictograph

A method of representing data visually using pictures, symbols, or icons, where a single symbol can represent a specific quantity.

Bar Graph

A graphical representation of data using rectangular bars of uniform width, where the length or height of the bars is proportional to the values they represent.

Scale

The chosen ratio or value that determines what unit measurement (or symbol) represents in a graph. For example, 1 unit length = 10 students.

Understanding Data Collection & Organisation

Data is a crucial resource in modern mathematics and everyday decision-making. When we first collect information, it is called raw data. Raw data can be highly confusing and hard to interpret directly. To make sense of it, we need systematic data organization. The most basic step is using a frequency table filled with tally marks, where every fifth count crosses the previous four lines diagonally to create clear bundles of five. Once organized, data can be displayed visually. Pictographs use symbols to represent quantities, which is highly intuitive but tedious for large numbers. For more professional and precise representations, we use bar graphs. A bar graph draws horizontal or vertical rectangular bars where the length of each bar is proportional to the quantity it represents. Choosing a correct scale is key to plotting an accurate bar graph.

Steps to Record and Organise Data using Tally Marks

1. Step 1: Collect Raw Data — Gather the unstructured list of observations (e.g., list of favorite fruits of 20 students).
2. Step 2: Create a Three-Column Table — Draw a table with three columns labeled: 'Category/Item', 'Tally Marks', and 'Frequency (Number)'.
3. Step 3: Apply Tally Marks — Go through the raw data one by one. For each occurrence, draw a vertical line (|) in the Tally Marks column. For the fifth occurrence, draw a diagonal line (/) across the first four vertical lines to make a bundle of 5 (卌).
4. Step 4: Write the Final Frequency — Count the tally bundles and individual lines for each item, write down the corresponding number in the Frequency column, and find the total sum.

Comparison: Pictograph vs. Bar Graph

Solved Revision Examples

• {"title":"Example 1: Recording Data via Tally Marks","description":"Organize the following test scores of 10 students using tally marks: 5, 7, 5, 8, 5, 7, 9, 8, 5, 7.","solution":"1. Identify unique scores: 5, 7, 8, 9.\n2. Count occurrences and draw tallies:\n- Score 5: 4 times -> ||||\n- Score 7: 3 times -> |||\n- Score 8: 2 times -> ||\n- Score 9: 1 time -> |\n3. Frequency Table:\n Score 5 | Tally: |||| | Frequency: 4\n Score 7 | Tally: ||| | Frequency: 3\n Score 8 | Tally: || | Frequency: 2\n Score 9 | Tally: | | Frequency: 1\n* Total Students = 4 + 3 + 2 + 1 = 10."}
• {"title":"Example 2: Reading a Pictograph","description":"A pictograph shows apple symbols representing fruits sold. If 1 apple symbol (🍎) = 10 actual apples, find the total apples sold if there are 4 and a half symbols printed.","solution":"- 1 full symbol (🍎) = 10 apples\n- 4 full symbols = 4 x 10 = 40 apples\n- 1 half symbol (broken apple) = 10 / 2 = 5 apples\n- Total apples sold = 40 + 5 = 45 apples."}

Must Remember - Key Revision Points

• Data collection is always done with a specific objective in mind.
• Tally marks are marked in bundles of 5. Four vertical strokes followed by a diagonal crossing stroke representing the fifth count.
• A pictograph represents data through pictures of objects. It helps in understanding data at a glance.
• In a pictograph, a key must always be defined to tell the reader what quantity one symbol represents.
• A bar graph consists of horizontal or vertical bars with equal spacing between them.
• The width of the bars in a bar graph has no numerical significance; only the length/height of the bar represents the value.
• The scale on a bar graph must be uniform throughout the axis (e.g., if 1 unit = 5 units, the next marks must be 10, 15, 20, etc.).
• Interpreting a graph means extracting useful conclusions by looking at the highs, lows, and trends of the bars/symbols.

Exam Tips & Common Mistakes to Avoid

• The 5th Tally Rule: Never draw 5 vertical lines and then cross them. The diagonal line is the fifth line itself. Four vertical lines plus one diagonal line equals five.
• Always Look at the Key: In pictograph questions, students often count the symbols directly and write that as the answer (e.g., writing '5' instead of '50' when 1 symbol = 10 units). Always multiply the number of symbols by the key value!
• Graph Margins and Labels: When drawing a bar graph, do not forget to label both axes (e.g., 'Subjects' on the X-axis and 'Marks' on the Y-axis) and write down the chosen scale in the top right corner. You will lose 1 mark if labels or the scale are missing!

Quick Revision Check

• What are tally marks, and why do we bundle them in groups of five? Tally marks are vertical lines used to record data quickly as it is collected. We bundle them in groups of five (four vertical and one diagonal) to make counting the final total easier and faster at a glance.
• If a bar graph scale is 1 unit length = 100 people, how long will a bar representing 450 people be? The bar length will be 4.5 units (since 450 / 100 = 4.5 units).
• Why is spacing between bars in a bar graph kept uniform? Uniform spacing is maintained because it ensures the graph looks organized and clean, preventing visual bias and making it easy to distinguish and compare different categories.
• Can a pictograph use fractional symbols? Explain with an example. Yes, a pictograph can use fractional or half symbols to represent values that are less than the full key unit. For example, if 1 book symbol = 10 books, then a half-book symbol represents 5 books.

Frequently Asked Questions