Data Chapter Notes | Year 6 Mathematics IGCSE (Cambridge) PDF Download

Bar charts, dot plots, waffle diagrams and pie charts

• Objective: Interpret and represent data in bar charts, dot plots, waffle diagrams, and pie charts, plan and carry out investigations using data in categories and with whole numbers, and predict outcomes, look for patterns, and check predictions.
• Key terms:
  • Bar chart: A graph using rectangular bars to represent the frequency of categories, with bar height proportional to the frequency.
  • Dot plot: A graph where each data point is represented by a dot above a number line, showing the frequency of occurrences.
  • Waffle diagram: A grid of squares (e.g., 100 squares) where each square represents a portion of the data, often used to show proportions.
  • Pie chart: A circular chart divided into sectors, where each sector represents a proportion of the total data.
  • Data: Information collected for analysis, often whole numbers or categorical in this context.
• Purpose of data representation:
  • Charts and graphs make it easier to identify patterns, trends, and relationships in data.
  • They facilitate clear communication of information to others.
• Bar charts:
  • Used to represent categorical data with frequencies.
  • Example: A bar chart showing the number of roses on bushes in ranges (e.g., 1-3, 4-6 roses).
  • Each bar’s height corresponds to the number of items in that category.
• Dot plots:
  • Show individual data points as dots above a number line.
  • Example: A dot plot showing test scores, where each dot represents a child’s score (e.g., 7 marks).
  • Useful for small datasets to visualize distribution and frequency.
• Waffle diagrams:
  • Represent proportions using a grid of squares (e.g., 100 squares for 100% or 20 squares for 20 items).
  • Example: A waffle diagram for 20 children’s favorite sports, where each square represents one child’s choice (e.g., football, basketball).
  • Proportions can be calculated as percentages (e.g., 5 squares out of 20 = 25%).
  • Equation: Percentage = (Number of squares / Total squares) × 100.
• Pie charts:
  • Show proportions of a whole as sectors of a circle.
  • Example: Representing favorite animals (elephant: 1, tiger: 2, giraffe: 2).
    • Total frequency: 1 + 2 + 2 = 5.
    • Divide a circle into 5 equal sections, each representing one animal.
    • Color each section according to a key (e.g., 1 section for elephant, 2 for tiger, 2 for giraffe).
  • Equation: Total frequency = 1 + 2 + 2 = 5.
  • Each sector’s angle can be calculated: Angle = (Frequency / Total frequency) × 360°.
• Data types:
  • Data in this section are whole numbers (e.g., number of peas in pods) or categorical (e.g., favorite sports).
  • Whole number data can be grouped into ranges for bar charts (e.g., 1-3 peas, 4-6 peas).
• Real-world applications:
  • Surveys (e.g., peas in pods, travel time to school).
  • Sports statistics (e.g., goals scored in matches).
  • Preference studies (e.g., favorite sports or drawing tools).
• Planning investigations:
  • Predict outcomes based on prior knowledge or assumptions.
  • Collect data in a frequency table to organize categorical or whole number data.
  • Choose appropriate representations (e.g., bar chart for comparing categories, pie chart for proportions).
  • Analyze patterns to confirm or refute predictions.

Frequency diagrams, line graphs and scatter graphs

• Objective: Interpret and represent data in frequency diagrams, line graphs, and scatter graphs, plan and carry out investigations using data that includes measures, and predict outcomes, look for patterns, and check predictions.
• Key terms:
  • Frequency diagram: A graph showing the frequency of data within specified intervals (e.g., speed of vehicles in km/h).
  • Line graph: A graph where data points are plotted and connected by straight lines, often used to show changes over time (e.g., temperature over hours).
  • Scatter graph: A graph where pairs of data are plotted as points to explore relationships between two variables (e.g., height vs. arm length).
• Purpose of these graphs:
  • Used to investigate links or trends between two sets of data, such as height and arm length or temperature and time.
  • Help visualize patterns, trends, or correlations in measured data (e.g., continuous data like speed, height, or pulse rate).
• Frequency diagrams:
  • Represent the frequency of data grouped into intervals.
  • Example: A frequency diagram showing vehicle speeds (e.g., 0-20 km/h, 20-40 km/h).
  • Data is collected and grouped into equal intervals, and the frequency (count) is plotted for each interval.
• Line graphs:
  • Show changes in data over a continuous variable, typically time.
  • Example: Temperature recorded every half hour by two thermometers, plotted as points connected by straight lines.
  • Example: Pulse rate measured every 10 minutes during and after a run, with points at times 0, 10, 20, ..., 80 minutes and pulse rates 66, 102, ..., 68 beats per minute.
  • Allow estimation of values between measured points (e.g., pulse rate at 15 minutes).
• Scatter graphs:
  • Plot pairs of data to explore relationships between two variables.
  • Example: Plotting hand span vs. foot length or plant height vs. number of leaves.
  • A line of best fit can be drawn to summarize the relationship:
    • The line should have the correct slope (not too steep or too flat).
    • It should pass through the middle of the points, with approximately equal numbers of points above and below.
    • Example: A scatter graph of father’s height vs. child’s height, with a line of best fit to show the trend.
  • Equation for line of best fit (conceptual): y = mx + c, where m is the slope and c is the y-intercept, adjusted to fit the data points.
• Data types:
  • Data in this section includes measures (continuous data) such as speed, height, temperature, pulse rate, or hand span, unlike categorical data in Section 15.1.
  • Example: Jump heights (e.g., 25 cm, 31 cm) or plant heights (e.g., 6 cm, 11 cm).
• Planning investigations:
  • Predict outcomes based on expected trends (e.g., higher temperatures may increase visitor numbers).
  • Collect data systematically, often in a table (e.g., time vs. pulse rate).
  • Choose appropriate graphs:
    • Frequency diagram for grouped continuous data (e.g., common heights).
    • Line graph for changes over time (e.g., water cooling).
    • Scatter graph for relationships between variables (e.g., height vs. test scores).
  • Analyze patterns to confirm or refute predictions (e.g., taller plants may have more leaves).
• Real-world applications:
  • Monitoring vehicle speeds near a school to assess traffic patterns.
  • Tracking temperature changes in different classroom locations.
  • Studying physiological changes, like pulse rate during exercise.
  • Investigating biological relationships, such as hand span vs. foot length or plant height vs. leaf count.
• Line of best fit criteria:
  • Correct slope: Matches the general trend of the data points.
  • Balanced position: Equal number of points above and below the line.
  • Used for estimation (e.g., estimating foot length for a 17 cm hand span using the line of best fit).