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Scientific Enquiry - Recording data in tables, bar charts, and line graphs

Grade 5Cambridge (IGCSE)

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

🔑Concepts

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Data tables are used to organize measurements systematically. The independent variable (what you change) is placed in the first column, and the dependent variable (what you measure) is placed in the subsequent columns. Units must be included in the header, not in every cell.

Structure of a scientific data table showing independent and dependent variables.
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Bar charts are used when the independent variable is 'categoric' or discrete (labels/words). The bars should be of equal width and separated by equal gaps.

A bar chart showing discrete categories on the x-axis and measurements on the y-axis.
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Line graphs are used for continuous data where both variables are numerical. Points should be plotted with an 'x' and connected with a line of best fit or smooth curve to show trends.

A line graph showing numerical data points plotted and connected by a line of best fit.
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Scales on axes must be linear, meaning they increase by the same amount for every grid square. The range of the scale should cover all data points and utilize at least half of the available graph paper.

📐Formulae

Mean=Sum of all data valuesTotal number of values\text{Mean} = \frac{\text{Sum of all data values}}{\text{Total number of values}}

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

Interval=Maximum Value on AxisNumber of Grid Squares\text{Interval} = \frac{\text{Maximum Value on Axis}}{\text{Number of Grid Squares}}

💡Examples

Problem 1:

A student measures the temperature of water every minute for 55 minutes as it cools. The readings are 80∘C80^{\circ}C, 75∘C75^{\circ}C, 70∘C70^{\circ}C, 66∘C66^{\circ}C, and 63∘C63^{\circ}C. Should this data be recorded in a bar chart or a line graph?

Solution:

A line graph.

Explanation:

Since time and temperature are both continuous variables, a line graph is the best way to show the trend of the water cooling over the 55 minute period.

Problem 2:

Calculate the mean (average) height of three plants measuring 12 cm12\text{ cm}, 15 cm15\text{ cm}, and 18 cm18\text{ cm}.

Solution:

Mean=15 cm\text{Mean} = 15\text{ cm}

Explanation:

Using the formula: 12+15+183=453=15 cm\frac{12 + 15 + 18}{3} = \frac{45}{3} = 15\text{ cm}

Problem 3:

In a data table for an experiment testing how the amount of water affects plant height, which column should 'Amount of Water (mlml)' be placed in?

Solution:

The first column (left side).

Explanation:

The amount of water is the independent variable (the factor being changed by the scientist), which by convention is placed in the first column of a data table.

Problem 4:

A researcher counts the number of insects found on different types of trees: Oak (15), Pine (8), and Birch (12). Draw a representation of how this data would be plotted on a bar chart and identify the independent variable.

Bar chart comparing insect counts on Oak, Pine, and Birch trees.

Solution:

The independent variable is 'Type of Tree'. The bar chart should show 'Type of Tree' on the xx-axis and 'Number of Insects' on the yy-axis with bars of heights 1515, 88, and 1212 respectively.

Explanation:

Because the tree types are discrete categories (names, not numbers), a bar chart is the correct choice. The height of each bar represents the frequency of insects.

Problem 5:

A student heats water and records the temperature every 22 minutes. The data points recorded are (0,20),(2,40),(4,60),(6,80)(0, 20), (2, 40), (4, 60), (6, 80). Plot these points on a graph and describe the relationship.

Line graph showing temperature increasing over time.

Solution:

The graph shows a linear relationship. For every 22 minute increase in time, the temperature increases by 20∘C20^{\circ}C. The formula for the temperature TT at time tt is T=10t+20T = 10t + 20.

Explanation:

Since both time and temperature are continuous numerical variables, a line graph is used. The points form a straight line, indicating a constant rate of heating.