How to Turn Raw Numbers into Clear Pictures

Handling and presenting data means collecting information, organising it in tables or charts, and showing it visually so it is easy to understand. In CBSE Class 6 Mathematics, you will learn how to collect data, use tally marks to make frequency tables, and present data using pictographs and bar graphs. This article covers all the key skills from Chapter 4: how to organise data, read and draw pictographs, and create and interpret bar graphs.

To collect and organise data, you first decide what question you want to answer, then record each response, and finally use tally marks to count how often each answer appears. Tally marks are quick lines grouped in sets of five, making it easy to count large numbers. You draw four vertical lines, then a diagonal fifth line across them to make a group of five. This is called a frequency table, where each row shows a category, its tally marks, and the total frequency (how many times it occurs).

For example, if you ask 20 classmates their favourite fruit and get: 7 apples, 5 bananas, 4 oranges, 4 mangoes, you make a table:

- Fruit: Apple | Tally: ||||| || | Frequency: 7
- Fruit: Banana | Tally: ||||| | Frequency: 5
- Fruit: Orange | Tally: |||| | Frequency: 4
- Fruit: Mango | Tally: |||| | Frequency: 4

A common mistake is to forget to group tally marks in fives, which makes counting harder. Tally marks help you see patterns quickly and prepare data for pictographs and bar graphs.

A pictograph uses pictures or symbols to show data, with each symbol standing for a certain number of items. To read a pictograph, check the key (which tells you what one symbol equals), count the symbols for each category, and multiply by the value of one symbol. To draw a pictograph, choose a symbol that is easy to repeat, decide what number it will represent, and clearly state the key.

For example, if you survey 12 students about their favourite sport and use one football symbol ⚽️ to represent 2 students, the pictograph for 6 students who like football would show 3 ⚽️ symbols. If cricket is liked by 4 students, you draw 2 🏏 symbols. Always write the key: '1 ⚽️ = 2 students'.

If the number doesn't divide exactly, you can use half a symbol. For example, 5 students would be 2 and a half symbols. Students often forget to write the key or draw symbols of different sizes, which makes the pictograph unclear. Always keep symbols the same size and explain your key.

To answer questions using a bar graph, look at the height or length of each bar to compare categories. The bar graph has two axes: one shows the categories, the other shows the numbers (scale). The tallest bar shows the largest value, and the shortest bar shows the smallest. You can find the difference between two bars by subtracting their values, and the total by adding up all bar heights.

For example, if a bar graph shows the number of books read by four friends: A (8), B (5), C (10), D (7), you can see C read the most books and B the least. The difference between C and B is 10 - 5 = 5 books. The total books read is 8 + 5 + 10 + 7 = 30 books.

A common mistake is to misread the scale or count the spaces instead of the bar heights. Always check the scale and count up to the top of each bar.

To draw a bar graph, choose a suitable scale for the number axis (for example, 1 square = 2 items), label both axes (categories and numbers), and draw bars of equal width with equal gaps between them. Each bar represents a category and its height shows the frequency. Start by drawing the axes, marking the scale, and writing the category names. Then, for each category, draw a bar up to the correct value. Keep all bars and gaps the same size for clarity.

For example, if you have data on the number of cars seen in four colours: Red (6), Blue (8), Green (4), Black (10), you could use a scale where 1 square = 2 cars. The Red bar would be 3 squares high, Blue 4, Green 2, and Black 5. Label the x-axis (Colour) and y-axis (Number of Cars).

A common trap is to make bars different widths or leave uneven gaps, making the graph hard to read. Uniform bars and clear labels make your graph easy to understand.