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Statistics and Data - Interpreting bar charts and pictograms

Grade 4IGCSE

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

🔑Concepts

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Bar Charts: Visual representations of data using rectangular bars where the length/height represents the value.

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The Scale: The numbers on the vertical axis (y-axis) that show the count. It often goes up in intervals of 2, 5, or 10.

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Pictograms: Using symbols or pictures to represent a set amount of data.

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The Key: A crucial part of a pictogram that explains what each symbol represents (e.g., 1 circle = 2 people).

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Partial Symbols: In pictograms, a half-symbol represents half the value of the key (e.g., if a star = 10, a half-star = 5).

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Data Interpretation: Using charts to find the most common (mode), the least common, the total count, or differences between categories.

📐Formulae

Total Value=Number of Symbols×Value in Key\text{Total Value} = \text{Number of Symbols} \times \text{Value in Key}

Difference=Value of Category A−Value of Category B\text{Difference} = \text{Value of Category A} - \text{Value of Category B}

Total Frequency=Sum of all category values\text{Total Frequency} = \text{Sum of all category values}

💡Examples

Problem 1:

In a pictogram, a symbol of a bicycle represents 44 students. If the 'Transport to School' chart shows 3123\frac{1}{2} bicycle symbols for Grade 4, how many students cycle to school?

Solution:

1414 students

Explanation:

Each full symbol is 44 students. 33 full symbols = 3×4=123 \times 4 = 12. The half symbol represents half of 44, which is 22. Total = 12+2=1412 + 2 = 14.

Problem 2:

A bar chart shows the favorite colors of students. The bar for 'Blue' reaches the line for 1515 and the bar for 'Red' reaches the line for 88. How many more students prefer Blue than Red?

Solution:

77 students

Explanation:

To find 'how many more', subtract the smaller value from the larger value: 15−8=715 - 8 = 7.

Problem 3:

Look at a bar chart where the scale on the y-axis goes up in steps of 55 (0,5,10,15...0, 5, 10, 15...). If a bar ends exactly halfway between 1010 and 1515, what is the value of that bar?

Solution:

12.512.5 (or 1212 or 1313 depending on context, usually 1212 or 1313 for discrete items)

Explanation:

Halfway between 1010 and 1515 is calculated by finding the middle point: (10+15)÷2=12.5(10 + 15) \div 2 = 12.5. In Grade 4, you identify this visually as being between the two marked intervals.