Section A — Chapters 1–22
Statistics II: Representing Data Graphically
Junior Cycle — 1st Year
- ✓By the end of this lesson students will be able to represent data using line plots, bar charts, and pie charts.
- ✓By the end of this lesson students will be able to construct and interpret stem-and-leaf plots for small datasets.
- ✓By the end of this lesson students will be able to draw and interpret histograms for continuous data.
- ✓By the end of this lesson students will be able to create and analyse trend graphs to show changes over time.
- ✓By the end of this lesson students will be able to select the most appropriate graphical representation for a given dataset.
Key concepts
A line plot (or dot plot) shows the frequency of data values along a number line. Each data value is represented by an 'X' or a dot placed above its corresponding number on the line. It is particularly useful for small datasets to quickly see the distribution.
A bar chart uses rectangular bars to represent the frequency or value of different categories of data. The length or height of each bar is proportional to the value it represents. Bars are typically separated by gaps and can be drawn vertically or horizontally. Bar charts are suitable for categorical or discrete data.
A pie chart is a circular graph divided into sectors, where each sector represents a proportion of the whole. The angle of each sector at the centre of the circle is proportional to the frequency or value it represents. Pie charts are used to show how a whole is divided into parts.
A stem-and-leaf plot is a method of organising numerical data by splitting each data point into a 'stem' (the leading digit(s)) and a 'leaf' (the trailing digit). It provides a visual representation of the distribution of the data while retaining the original data values. A key is essential to interpret the plot.
A histogram is similar to a bar chart but is used to represent continuous data that has been grouped into class intervals. The bars in a histogram are drawn without gaps, indicating the continuous nature of the data. The width of each bar represents the class interval, and the height represents the frequency of data within that interval.
A trend graph, also known as a line graph, displays data points connected by line segments. It is primarily used to show how data changes over a continuous period, such as time. Time is typically plotted on the horizontal (x) axis, and the measured quantity on the vertical (y) axis.
The choice of chart depends on the type of data and the message you want to convey:\n- **Line Plot**: Small discrete datasets, to show frequency of individual values.\n- **Bar Chart**: Categorical or discrete data, for comparing quantities across different categories.\n- **Pie Chart**: To show parts of a whole, proportions or percentages.\n- **Stem-and-leaf Plot**: Small to medium numerical datasets, to show distribution and retain original values.\n- **Histogram**: Continuous numerical data, grouped into intervals, to show distribution.\n- **Trend Graph**: Data that changes over time, to show patterns or trends.
Key facts to remember
- 1Graphs and charts are visual tools that make data easier to understand, interpret, and compare.
- 2A line plot uses 'X's or dots above a number line to show the frequency of individual data values.
- 3Bar charts use separate bars to compare quantities across different categories of data.
- 4Pie charts illustrate parts of a whole, with the size of each sector proportional to its share of the total.
- 5Stem-and-leaf plots organise numerical data, showing its distribution while preserving the original values; a key is always required.
- 6Histograms use contiguous (touching) bars to represent the frequency distribution of continuous data grouped into class intervals.
- 7Trend graphs (line graphs) are used to display how data changes or trends over a continuous period, typically time.
- 8All graphs must have a clear title and properly labelled axes (and a key for stem-and-leaf plots) to be easily understood.
Worked examples
Example 1
A class of 20 students voted for their favourite fruit. The results were: Apple (8), Banana (6), Orange (4), Grape (2). Represent this data using a bar chart and calculate the angle for the 'Apple' sector in a pie chart.
Answer
Bar Chart: A vertical bar chart with 'Fruit' on the x-axis and 'Number of Students' on the y-axis, showing bars of heights 8 (Apple), 6 (Banana), 4 (Orange), and 2 (Grape), with gaps between bars and a title. \nPie Chart (Apple sector): The angle for the Apple sector is 144°.
Remember to label all axes and provide a title for every graph. For pie charts, ensure all angles add up to 360°.
Example 2
The ages of 15 people attending a workshop are: 23, 31, 28, 45, 30, 29, 33, 41, 25, 37, 22, 30, 48, 26, 35. Construct a stem-and-leaf plot for this data.
Answer
2 | 2 3 5 6 8 9\n3 | 0 0 1 3 5 7\n4 | 1 5 8\nKey: 2 | 2 = 22 years
A stem-and-leaf plot allows you to see the shape of the distribution while keeping the original data values. Always include a key.
Example 3
The average monthly temperatures (°C) in Dublin for the first six months of a year were: January (5), February (6), March (8), April (10), May (13), June (16). Draw a trend graph to show this data.
Answer
A line graph with 'Month' on the x-axis (Jan, Feb, Mar, Apr, May, Jun) and 'Temperature (°C)' on the y-axis. Points (Jan,5), (Feb,6), (Mar,8), (Apr,10), (May,13), (Jun,16) are plotted and connected by straight lines, with a clear title.
Trend graphs are excellent for showing how data changes over time. Ensure the time intervals on the x-axis are consistent.
Common mistakes
- ✗Not labelling axes or providing a title for the graph, making it difficult to understand.
- ✗Using inconsistent or inappropriate scales on the axes, which can distort the data's representation.
- ✗Drawing gaps between bars in a histogram (for continuous data) or drawing bars without gaps in a bar chart (for categorical data).
- ✗Forgetting to include a key for stem-and-leaf plots, making the plot uninterpretable.
- ✗Incorrectly calculating the angles for sectors in a pie chart, leading to an inaccurate representation of proportions.
- ✗Confusing bar charts (for categorical/discrete data) with histograms (for continuous data).
Exam tips
- ★Always read the question carefully to determine the most suitable type of graph or chart required.
- ★Use a ruler and a sharp pencil for all drawings to ensure neatness, accuracy, and clarity.
- ★Double-check all calculations, especially when determining angles for pie charts or frequencies for histograms.
- ★Ensure your graph has a clear, descriptive title and that all axes are correctly labelled with units where appropriate.
- ★For stem-and-leaf plots, make sure the leaves are ordered numerically for each stem and that a key is always present.
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