Pictorial and Graphical Representation of Data
Which diagram, and why that one? Match the representation to the data, read what it shows, and learn the histogram rule that decides whole questions.
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Which diagram, and why? 📊
This part of the course looks like a list of chart names to memorise. It is not. Almost every question comes down to one thing: **does this representation suit this data, and what does it show?** So learn each diagram with the data type it belongs to. A representation that is right for categories is wrong for continuous measurements, and an examiner will always know which you were given.
Two big families 🗂️
Most of the diagrams in this section fall into one of two jobs. Getting the job right narrows the choice immediately.
Match each task to the representation that suits it
- Showing what share of a budget each department takes
- Showing how monthly sales changed across two years
- Investigating whether two variables are related
- Showing how many students take both Statistics and Geography
- A pie chart
- A time series graph
- A scatter diagram
- A Venn diagram
Continuous and grouped 📈
You have the heights of 200 people, grouped into classes of equal width. Which representation is designed for exactly this?
- A histogram, with the bars touching
- A bar chart, with gaps between the bars
- A pie chart
- A pictogram
What is Higher only, and the rule that matters ⚠️
Some of this sub-section is Higher tier only, so check which paper you are sitting: • Comparative pie charts, and comparative 2D and 3D representations • **Frequency density**, and histograms with UNEQUAL class widths • Skewness by CALCULATION, where the formula is given **The rule worth more than the list:** once the class widths are unequal, the height of each bar is no longer the frequency. It is the **frequency density**, which is frequency divided by class width, and the FREQUENCY IS THE AREA of the bar. Reading a height as a frequency on an unequal-width histogram loses the whole question.
Histograms ✅
Select the TWO correct statements about histograms.
- The bars touch, because the horizontal scale is continuous
- When class widths are unequal, the frequency is represented by the AREA of each bar
- The height of a bar always gives the frequency, whatever the class widths
- A histogram is the right choice for separate named categories
The specialist four 🌡️
These come up precisely because they are distinctive. Each exists to do one job well:
Match each specialist diagram to what it is for
- Back-to-back stem-and-leaf
- Population pyramid
- Choropleth map
- Two-way table
- Comparing two groups while keeping every original value
- Showing the age and sex structure of a population
- Showing how a value varies from region to region
- Cross-classifying counts by two categorical variables
Find the tail 🎯
An interactive activity.
Which way is it skewed? ↩️
That distribution peaks near the left and trails away to the right. What is it called?
- Positively skewed, because the tail runs to the right
- Negatively skewed, because the peak is on the left
- Symmetrical, since it has one clear peak
- It has no skew, because skew only applies to histograms
Draw the pie chart 🥧
An interactive activity.
The summary 📝
Separate categories get a bar chart, with _____ between the bars; grouped continuous data gets a _____, with the bars touching. When class widths are unequal the bar height is the _____ and the frequency is the _____ of the bar. A distribution whose tail runs to the right is _____ skewed.
Choose and justify ✍️
An interactive activity.