Data Handling and Presentation
Information collected as numbers or facts is called data. This Class 6 Ganita Prakash chapter shows how to organise data using tally marks and tables, present it as pictographs and bar graphs, and read useful information back out of these pictures.
Learning objectives
- Collect and organise data into a table.
- Record data using tally marks.
- Read and draw pictographs and bar graphs.
- Interpret information from a data display.
Key concepts
Data and tally marks
Data is a collection of facts or numbers gathered for a purpose, such as the favourite fruits of a class. To count quickly we use tally marks, drawing one stroke per item and crossing every fifth one, so groups of five are easy to total.
Organising data in a table
Raw data is hard to read, so we organise it into a frequency table that lists each category beside how many times it occurs (its frequency). A clear table makes comparisons and totals straightforward.
Pictographs
A pictograph shows data using a symbol or picture to stand for a fixed number of items. A key tells the value of one symbol, so if one apple picture means 5 apples, three pictures mean 15 apples. Half a symbol shows half that value.
Bar graphs
A bar graph uses bars of equal width whose heights (or lengths) represent the frequencies. Taller bars mean larger values, so a bar graph makes it easy to compare categories at a glance and to read each value against the scale.
Important formulas
Pictograph value
value = number of symbols × value of one symbol
Key definitions
- Data
- A collection of facts or numbers gathered for a purpose.
- Tally marks
- Strokes used to count, grouped in fives for easy totalling.
- Frequency
- The number of times a value or category occurs.
- Pictograph
- A display that represents data using pictures or symbols.
Solved examples
Q1. How is the number 7 shown in tally marks?
Solution: One group of five (four strokes crossed) followed by two more strokes.
Q2. In a pictograph, one star = 10 books. How many books do 4 stars show?
Solution: 4 × 10 = 40 books.
Q3. In a bar graph, which category is most popular?
Solution: The one shown by the tallest (longest) bar.
Common mistakes to avoid
- Forgetting the key when reading a pictograph.
- Drawing bars of unequal width in a bar graph.
- Miscounting tally marks by ignoring the grouping of five.
- Reading a bar's height against the wrong scale marking.
Data Handling and Presentation — MCQ Quiz
10 questions with instant feedback. Use number keys 1–4 to answer.
A collection of facts or numbers is called:
Practice questions
Short answer
Why do we use tally marks?
To count quickly, grouping strokes in fives for easy totalling.
What does the key of a pictograph tell us?
How many items one symbol stands for.
What does the height of a bar in a bar graph represent?
The frequency or value of that category.
Long answer
Explain how a pictograph is made and read, with an example.
A pictograph represents data using a symbol that stands for a fixed number of items, stated in a key. To make one, choose a symbol and a suitable value (say one book picture = 10 books), then draw the right number of symbols for each category, using a part-symbol for part of the value. To read it, multiply the number of symbols by the key value: if 'fiction' shows 3½ book symbols and one symbol means 10 books, that is 3½ × 10 = 35 books.
Compare a bar graph and a pictograph as ways of presenting data.
Both turn a table of frequencies into a picture that is easier to compare. A pictograph uses repeated symbols with a key, which is friendly and visual but awkward for values that are not neat multiples of the key. A bar graph uses bars of equal width whose heights are read against a scale, which handles any value precisely and makes comparing categories very quick. Bar graphs are usually clearer for larger or uneven numbers, while pictographs are appealing for simple data.
HOTS (Higher Order Thinking)
In a pictograph one symbol = 8 mangoes. A row has 2½ symbols. How many mangoes is that?
2½ × 8 = 20 mangoes.
Why must all bars in a bar graph have equal width?
So that only the height shows the value; unequal widths would make comparison misleading.
Quick revision
Revision notes
- Data = collected facts/numbers; organise in a frequency table.
- Tally marks group in fives.
- Pictograph: symbols with a key; value = symbols × key.
- Bar graph: equal-width bars; height = value.
Key takeaways
- Organising data makes it easy to read and compare.
- A pictograph always needs a key.
- Bar height (not width) carries the value.
Frequently asked questions
What is data?
A collection of facts or numbers gathered for a purpose.
What is frequency?
How many times a value or category occurs.
What is the difference between a pictograph and a bar graph?
A pictograph uses symbols with a key; a bar graph uses bars read against a scale.