Sub-Topic I: Pictorial Representations

Tabulation: Helps organize data, making it easier to understand.

Tally: Use tallies to count frequencies (e.g.,  ∣∣∣∣ for 4).

Pictogram: Uses symbols to represent quantities.

Pie Charts: Should be used when wanting to see proportions.

Stem and Leaf Diagram: Shows the distribution of data.

Back-to-Back Stem and Leaf Diagram: Displays two related datasets using a common stem.

Population Pyramid: Shows the demographic distribution (age and sex) using a bar chart.

Choropleth Map: Displays geographic information, shaded in proportion to a statistical variable.

Venn Diagram: Shows all possible logical relations between a finite collection of sets.

Sub-Topic II: Graphical Representations

• Bar Charts: Uses rectangular bars to represent the frequency or value of categories.

• Line Charts: Plots data points connected by straight lines to show trends over time.

• Time Series: A sequence of data points typically measured at successive points in time.

• Scatter Charts: Plots data points on a Cartesian plane to show relationships between two variables.

• Bar Line Charts: Combination of bar and line charts to show different aspects of the data.

• Frequency Polygons: A line graph of the frequency distribution/distribution of data.

• Cumulative Frequency Charts: Shows the cumulative totals of data points.

• Histograms (Equal Width): Displays frequency distributions with bars of equal width.
  $\text{Histogram Bar Height} = \frac{\text{Frequency}}{\text{Class Width}}$

• Box Plots: Shows the distribution of data based on minimum, first quartile (Q1), median, third quartile (Q3), and maximum.

• Histograms (Unequal Width): Displays frequency distributions with bars of varying width.

$\text{Frequency Density} = \frac{\text{Frequency}}{\text{Class Width}}$

Sub-Topic III: Justification and Accuracy

In choosing and justifying your type of data for data visualization, you’ll want to follow this

• Categorical Data: Use pie charts, bar charts, or pictograms. These formats help visualize the proportion of each category.

• Quantitative Data: Use histograms, line charts, or box plots to show distribution, trends, or variability.

• Time Series Data: Line charts or time series plots are ideal for showing trends over time.

• Comparative Data: Use bar charts or comparative pie charts to compare different categories or groups.

  • Aim to focus on 2D info, (e.g.dual, multiple, and composite bar types)

Example I:

Data on the number of students in different clubs at school:

• Data: 50 students in the Science Club, 30 in the Drama Club, and 20 in the Art Club.

• Visualization Choice:

  • Bar Chart: Suitable for comparing the number of students in each club.

  • Pie Chart: Effective for showing the proportion of students in each club.

• Identify Data Type: Categorical data (clubs).

• Select Visualization: Bar chart to compare the absolute numbers, pie chart to show proportions.

• Justify Choice: Both formats effectively represent the data, but the pie chart emphasizes proportions, while the bar chart highlights absolute values.

Sub-Topic IV: Data Comparison & Representation

Median: The middle value when data is ordered.

$\text{Median} = \text{Middle Value}$

• If there is an even number of data points, the median is the average of the two middle values.

Interquartile Range (IQR): Difference between the first and third quartiles.

$\text{IQR} = Q3 - Q1$

Mean: Average of the data.

$\bar{x} = \frac{\sum{x}}{n}$

Standard Deviation: Measure of data dispersion.

$\sigma = \sqrt{\frac{\sum{(x - \bar{x})^2}}{n}}$

• The Standard Deviation helps in understanding how spread out the data is from the mean.

Important Information (as per AQA GCSE)

• GCSE exam will not include exam-takers/students to draw 3D representations

• Sub-Topic II: includes dual, multiple, composite, and percentage bar charts. Includes cumulative frequency step polygons for discrete data.

• Sub-Topic III: justifications include, but are not limited to, the type of data

  • students will be expected to critique graphical misrepresentation from secondary sources.

• Sub-Topic IV: students should be able to, for example, compare medians and interquartile ranges or means and standard deviations. These may be given or may have to be calculated.