Trend Graphs

Overview

A trend chart (or line graph) is a graphical representation used to display data points in a sequential order, typically over time. It helps illustrate patterns or trends in the data, making it an essential tool for analysing how a variable changes.

Key Features of Trend Charts

Axes:

Horizontal axis $(x-axis):$ Represents the independent variable, usually time.
Vertical axis $(y-axis):$ Represents the dependent variable or the data being measured.

Data Points:

Each point represents a specific measurement or observation.
Points are connected by lines to visualise trends over the given range.

Trends:

Increasing trend: The line rises, indicating growth or increase.
Decreasing trend: The line falls, indicating a decline.
Steady trend: The line is flat, indicating no change.

Multiple Data Sets:

Trend charts can compare multiple data sets by plotting different lines on the same graph.

Examples

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Example 1: Temperature Over a Week

Problem:

A city records daily temperatures for a week as follows:

Monday: 18°C
Tuesday: 20°C
Wednesday: 22°C
Thursday: 19°C
Friday: 21°C
Saturday: 23°C
Sunday: 24°C Create a trend chart to display this data.

Solution:

Step 1: Identify axes:

$x-axis :$ Days of the week.
$y-axis:$ Temperature (in °C)

Step 2: Plot data points:

Monday: (1, 18), Tuesday: (2, 20), ..., Sunday: (7, 24)

Step 3: Connect points:

Draw lines connecting consecutive points to show the trend.

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Example 2: Monthly Sales Data

Problem:

A company tracks its monthly sales (in thousands) as follows:

January: £50k
February: £55k
March: £60k
April: £65k
May: £70k Create a trend chart to represent this data.

Solution:

Step 1: Identify axes:

$x-axis:$ Months (January to May).
$y-axis:$ Sales (in £k).

Step 2: Plot data points:

January: (1, 50), February: (2, 55), ..., May: (5, 70).

Step 3: Connect points:

Draw lines to connect consecutive points.

The trend shows consistent growth in sales from January to May.

Summary

A trend chart uses lines to connect data points, making it ideal for showing patterns over time.
Key components include axes ( $x-axis$ for independent variable, $y-axis$ for dependent variable), data points, and lines.
Trends can indicate growth, decline, or stability.
Trend charts can compare multiple data sets on the same graph.
Steps to create a trend chart:
1. Identify the variables and axes.
2. Plot data points.
3. Connect the points with lines.
4. Interpret the trends to draw conclusions.

Trend Graphs Simplified Revision Notes for Leaving Cert Mathematics