krit.club logo

Data Handling - Bar Graphs and Pictograms

Grade 3IB

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

•

Data Collection and Tally Marks: Data is information gathered through counting or measuring. Tally marks are vertical lines used for counting, where every fifth mark is drawn diagonally across the first four ∣∣∣∣\cancel{||||} to represent a group of 55. This helps in counting large numbers quickly by skip-counting by 5s5s.

•

Pictograms: A pictogram uses symbols or pictures to represent a set of data. For example, a picture of a smiley face ⊙\odot might represent 22 students. These charts help us visualize which category has the most or least items based on the number of symbols shown.

•

The Key (Legend): Every pictogram must have a 'Key' which explains the value of one symbol. If the key says 11 tree symbol =10= 10 trees, then 33 tree symbols represent 3×10=303 \times 10 = 30 trees. Visualizing a 'half-symbol' usually means half the value indicated in the key.

•

Bar Graphs: A bar graph uses rectangular bars to show data. The bars can be vertical (standing up) or horizontal (lying down). The height or length of the bar represents the frequency (how many) of that category. All bars must have the same width and be spaced equally apart.

•

Axes and Labels: Bar graphs have two lines called axes. The horizontal axis (x-axis) usually shows categories (like 'Types of Fruit'), and the vertical axis (y-axis) shows the numbers (the scale). Both axes must have clear labels to describe what is being measured.

•

Scale and Intervals: The scale is the set of numbers marked at regular intervals along the side of a bar graph. Instead of counting by 1s1s, the scale might jump by 2s,5s, or 10s2s, 5s, \text{ or } 10s. For example, a scale might be marked 0,5,10,15,200, 5, 10, 15, 20. If a bar ends halfway between 1010 and 1515, its value is 12.512.5 or 1313.

•

Interpreting Data: This involves reading the graph to answer questions. We can find the 'Mode' (the category with the tallest bar or most symbols), calculate the 'Total' by adding all values together, or find the 'Difference' by comparing the heights of two different bars.

📐Formulae

Total Value in Pictogram=Number of Symbols×Value per Symbol\text{Total Value in Pictogram} = \text{Number of Symbols} \times \text{Value per Symbol}

Difference Between Categories=Higher Value−Lower Value\text{Difference Between Categories} = \text{Higher Value} - \text{Lower Value}

Total Frequency=Value1+Value2+Value3+…\text{Total Frequency} = \text{Value}_1 + \text{Value}_2 + \text{Value}_3 + \dots

Value of Half Symbol=Value of Full Symbol2\text{Value of Half Symbol} = \frac{\text{Value of Full Symbol}}{2}

💡Examples

Problem 1:

In a pictogram about favorite ice cream flavors, the Key states: 11 ice cream cone symbol =4= 4 children. If the 'Vanilla' category has 33 full symbols and 11 half-symbol, how many children chose Vanilla?

Solution:

Step 1: Identify the value of a full symbol from the key: 1 symbol=4 children1 \text{ symbol} = 4 \text{ children}. Step 2: Calculate the value of the half-symbol: 4÷2=2 children4 \div 2 = 2 \text{ children}. Step 3: Calculate the total for 33 full symbols: 3×4=12 children3 \times 4 = 12 \text{ children}. Step 4: Add the half-symbol value to the total: 12+2=1412 + 2 = 14.

Explanation:

To solve pictogram problems, first look at the key. Multiply the number of whole symbols by the value in the key, then add the fractional value of any partial symbols.

Problem 2:

A bar graph shows the number of books read by three students: Maya read 1515 books, Arjun read 1010 books, and Sam read 2525 books. If the scale on the y-axis goes up in intervals of 55, how much higher will Sam's bar be compared to Arjun's bar?

Solution:

Step 1: Find the value for Sam: 25 books25 \text{ books}. Step 2: Find the value for Arjun: 10 books10 \text{ books}. Step 3: Calculate the difference in books: 25−10=15 books25 - 10 = 15 \text{ books}. Step 4: Determine the difference in 'bar segments' based on the scale: Since each interval is 55, the height difference is 15÷5=3 intervals15 \div 5 = 3 \text{ intervals}.

Explanation:

The problem asks for the comparison between two bars. We find the numerical difference first (1515). Since the graph's scale increments by 55 units per grid line, Sam's bar will be 33 grid lines higher than Arjun's.