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Statistics and Data - Interpreting and constructing line graphs

Grade 4Cambridge (IGCSE)

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

🔑Concepts

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Line graphs are used to show how data changes over time. They consist of two axes: the horizontal x-axis (usually time) and the vertical y-axis (the measured variable). Points are plotted and connected with straight lines to show the trend.

A basic line graph showing a fluctuating upward trend over time.
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The steepness of the line indicates the rate of change. A steep line means a rapid increase or decrease, while a flat line means the value remained constant over that interval.

Comparison of a steep line segment (rapid change) and a flat line segment (no change).
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Interpreting points involves looking directly across to the y-axis for values and down to the x-axis for specific times. To find a difference, subtract the initial value from the final value.

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When constructing a line graph, choose a scale for the y-axis that covers the entire range of data. Ensure intervals are equal, such as counting in 2s2s, 5s5s, or 10s10s.

📐Formulae

Interval Size=Highest ValueNumber of Grid Lines\text{Interval Size} = \frac{\text{Highest Value}}{\text{Number of Grid Lines}}

Difference in Value=Value at Time 2−Value at Time 1\text{Difference in Value} = \text{Value at Time 2} - \text{Value at Time 1}

Trend=Direction of the line (Upward/Downward/Flat)\text{Trend} = \text{Direction of the line (Upward/Downward/Flat)}

💡Examples

Problem 1:

A line graph shows the temperature in a classroom. At 09:00, the temperature was 18∘C18^{\circ}C. At 12:00, the line rises to 24∘C24^{\circ}C. What is the increase in temperature between 09:00 and 12:00?

Solution:

24∘C−18∘C=6∘C24^{\circ}C - 18^{\circ}C = 6^{\circ}C

Explanation:

To find the increase, identify the values on the y-axis for both time points on the x-axis and subtract the earlier value from the later value.

Problem 2:

On a graph tracking a seedling's height, the points are: Day 1 (2cm), Day 2 (4cm), Day 3 (6cm). If the trend continues, what will the height be on Day 5?

Solution:

10cm

Explanation:

The graph shows a steady increase of 2cm per day. To find the value for Day 5, we continue the pattern: Day 4 would be 6+2=8cm6 + 2 = 8cm, and Day 5 would be 8+2=10cm8 + 2 = 10cm.

Problem 3:

If the y-axis of a graph starts at 0 and has 5 equal intervals reaching up to 50, what is the value of each grid line?

Solution:

10 units per line

Explanation:

To find the scale interval, divide the total range by the number of intervals: 50÷5=1050 \div 5 = 10.

Problem 4:

The graph shows the volume of water in a tank over 4 hours. How much water was lost between Hour 2 and Hour 3?

Line graph showing volume decreasing from 15L at hour 2 to 5L at hour 3.

Solution:

15 L−5 L=10 L15\text{ L} - 5\text{ L} = 10\text{ L}

Explanation:

Identify the volume at Hour 2, which is 15 L15\text{ L}. Identify the volume at Hour 3, which is 5 L5\text{ L}. The difference is 15−5=10 L15 - 5 = 10\text{ L}.

Problem 5:

A car travels at a steady speed. Plot the distance covered: 0 mins (0 km0\text{ km}), 10 mins (10 km10\text{ km}), 20 mins (20 km20\text{ km}), 30 mins (30 km30\text{ km}). What is the distance at 25 minutes?

Linear graph showing distance increasing at 1km per minute.

Solution:

25 km25\text{ km}

Explanation:

The points (0,0),(10,10),(20,20),(30,30)(0,0), (10,10), (20,20), (30,30) form a straight diagonal line. By finding 25 on the time axis and moving up to the line, the corresponding distance on the y-axis is 25 km25\text{ km}.

Interpreting and constructing line graphs Grade 4 Notes & Examples