krit.club logo

Data Handling and Probability - Interpreting and drawing line graphs

Grade 5Cambridge (IGCSE)

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

🔑Concepts

•

Line graphs are used to show how data changes over time. They are created by plotting points on a grid and connecting them with straight line segments.

A basic line graph showing points connected by lines on a coordinate plane.
•

The steepness of the line (gradient) indicates the rate of change. A steeper line means a faster increase or decrease, while a horizontal line shows no change (00 change) over time.

Comparison of a steep line representing fast change and a horizontal line representing no change.
•

The x-axis usually represents the independent variable (often time, such as hours, days, or months), and the y-axis represents the dependent variable (the quantity being measured).

Standard axes for a line graph with labels for time and measurement.
•

When interpreting a graph, look for trends: an upward trend shows growth, while a downward trend shows a decrease. Fluctuations indicate inconsistent change.

📐Formulae

Interval Size=Highest ValueNumber of intervals on the axis\text{Interval Size} = \frac{\text{Highest Value}}{\text{Number of intervals on the axis}}

Value Difference=New Value−Original Value\text{Value Difference} = \text{New Value} - \text{Original Value}

Range=Highest Value−Lowest Value\text{Range} = \text{Highest Value} - \text{Lowest Value}

💡Examples

Problem 1:

A line graph shows a plant's height was 4 cm on Monday and 10 cm on Friday. What was the growth over these 5 days?

Solution:

10 cm−4 cm=6 cm10\text{ cm} - 4\text{ cm} = 6\text{ cm}

Explanation:

To find the change or growth, subtract the starting value (Monday) from the ending value (Friday). The plant grew 6 cm.

Problem 2:

You are plotting temperature data where the highest temperature is 35°C. If your Y-axis has 7 major grid squares, what should each interval represent?

Solution:

35÷7=535 \div 7 = 5

Explanation:

Divide the maximum value by the number of squares available to find a suitable scale. Each grid line should represent 5°C.

Problem 3:

In a graph representing a car's journey, the line is perfectly horizontal between 2:00 PM and 2:30 PM. What does this tell you about the car's movement?

Solution:

The car was stationary (stopped).

Explanation:

A horizontal line on a distance-time graph indicates that the distance is not changing as time passes, meaning the object is at rest.

Problem 4:

The following graph shows the temperature recorded in a garden from 8 AM to 12 PM. What is the difference between the temperature at 9 AM and 11 AM?

Temperature graph showing values increasing from 16 to 28 degrees over 4 hours.

Solution:

  1. At 9 AM (x=1), the temperature is 1818°C.
  2. At 11 AM (x=3), the temperature is 2424°C.
  3. Difference=24−18=6\text{Difference} = 24 - 18 = 6°C.

Explanation:

To find the difference, locate the time on the x-axis, find the corresponding y-value on the line, and subtract the smaller value from the larger one.

Problem 5:

A water tank is being filled. The depth of water at 1 minute is 1010 cm and at 4 minutes it is 4040 cm. If the filling rate is constant, draw the line and determine the depth at 3 minutes.

A straight line graph showing water depth increasing over time.

Solution:

  1. Plot point (1,10)(1, 10) and point (4,40)(4, 40).
  2. Connect the points with a straight line.
  3. Locate 33 minutes on the x-axis and read the y-value: 3030 cm. Depth at 3 minutes=30 cm\text{Depth at 3 minutes} = 30 \text{ cm}

Explanation:

Since the rate is constant, the graph is a straight line. We can use the plotted line to 'interpolate' (find values within the data range).