IB MYP 4-5 Maths- Graphical representations- Study Notes - New Syllabus
IB MYP 4-5 Maths- Graphical representations – Study Notes
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- Graphical representations
IB MYP 4-5 Maths- Graphical representations – Study Notes – All topics
Graphical Representations
Graphical Representations
Graphical representation of data is the process of presenting numerical data visually using charts or graphs. This helps identify patterns, trends, and relationships quickly.
Why use Graphs?
- Makes data easier to understand and interpret.
- Helps identify trends and relationships between variables.
- Used for comparison and decision-making.
Main Types of Graphs in MYP:
- Bivariate Graphs: Show the relationship between two variables (e.g., time vs distance).
- Scatter Graphs: Show how two continuous variables relate and can indicate correlation.
- Box Plots (Box-and-Whisker): Show distribution using median, quartiles, and outliers.
- Cumulative Frequency Graphs: Show how cumulative totals build up, useful for medians and percentiles.
Bivariate Graphs
Bivariate Graphs
A bivariate graph shows the relationship between two variables plotted on a coordinate plane. One variable is placed on the x-axis (independent) and the other on the y-axis (dependent).
Key Features:
- Helps visualize the connection between two quantities.
- Usually plotted as points or a line graph when the data is continuous.
- Common in real-life: time vs speed, age vs height.
Example:
The table shows time (minutes) and distance (km) traveled by a cyclist:
| Time (minutes) | Distance (km) |
|---|---|
| 0 | 0 |
| 10 | 5 |
| 20 | 10 |
| 30 | 15 |
| 40 | 20 |
Draw a bivariate graph and describe the relationship.
▶️Answer/Explanation
Step 1: Plot time on the x-axis and distance on the y-axis.
Step 2: Plot points (0,0), (10,5), (20,10), (30,15), (40,20).
Step 3: Join with a straight line – this shows a linear relationship.
Answer: The graph shows direct proportionality: as time increases, distance increases at a constant rate.
Example:
The table shows the temperature at different times of the day:
| Time | Temperature (°C) |
|---|---|
| 6 am | 16 |
| 9 am | 20 |
| 12 pm | 26 |
| 3 pm | 24 |
| 6 pm | 18 |
Plot a bivariate line graph and interpret the pattern.
▶️Answer/Explanation
Step 1: Convert time into numerical values (6, 9, 12, 15, 18).
Step 2: Plot points and connect smoothly.
Interpretation: Temperature rises in the morning, peaks at noon, then decreases towards evening.
Scatter Graphs
Scatter Graphs
A scatter graph (or scatter plot) shows the relationship between two numerical variables by plotting points on a coordinate plane. It is used to check for correlation between variables.
Key Features:
- Each point represents one pair of values (x, y).
- Used to check for a correlation between two variables.
- We can draw a line of best fit to show the trend.
Types of Correlation:
- Positive correlation: As one variable increases, the other also increases.
- Negative correlation: As one variable increases, the other decreases.
- No correlation: No pattern or relationship between the two variables.
Line of Best Fit:
- A straight line drawn through the points, showing the overall trend.
- Helps predict values of one variable based on the other.
Example:
The table shows the number of hours studied and the marks scored by 8 students:
| Hours Studied | Marks (%) |
|---|---|
| 1 | 45 |
| 2 | 50 |
| 3 | 58 |
| 4 | 62 |
| 5 | 70 |
| 6 | 74 |
| 7 | 78 |
| 8 | 85 |
Draw a scatter graph and describe the correlation.
▶️Answer/Explanation
Step 1: Plot points (Hours, Marks) on a graph.
Step 2: Observe the pattern: points rise upwards from left to right.
Step 3: Draw a line of best fit through the data points.
Answer: There is a strong positive correlation between hours studied and marks scored.
Example:
The table shows the daily temperature and the number of hot drinks sold:
| Temperature (°C) | Hot Drinks Sold |
|---|---|
| 5 | 120 |
| 8 | 110 |
| 10 | 95 |
| 12 | 85 |
| 15 | 70 |
| 18 | 55 |
Draw a scatter graph and describe the correlation.
▶️Answer/Explanation
Step 1: Plot points (Temperature, Drinks sold) on a graph.
Step 2: Observe pattern: as temperature increases, hot drink sales decrease.
Step 3: Draw a downward-sloping line of best fit.
Answer: There is a strong negative correlation between temperature and hot drinks sold.
Box Plots (Box-and-Whisker)
Box Plots (Box-and-Whisker)
A box plot is a diagram that shows the distribution of a data set using five key values: minimum, lower quartile (Q1), median (Q2), upper quartile (Q3), and maximum. It helps visualize the spread and detect outliers.
Key Features:
- The box represents the interquartile range (IQR) = Q3 − Q1.
- A line inside the box marks the median.
- Whiskers extend to the smallest and largest data values.
- Shows symmetry, skewness, and spread of data.
Steps to Draw a Box Plot:
- Arrange data in ascending order.
- Find:
- Minimum and Maximum
- Median (Q2)
- Lower quartile (Q1): median of the lower half
- Upper quartile (Q3): median of the upper half
- Draw a scale and plot these five values.
- Draw the box from Q1 to Q3 and whiskers to min and max.
Example:
The marks (out of 50) scored by 9 students are:
| Marks |
|---|
| 12 |
| 15 |
| 18 |
| 20 |
| 24 |
| 26 |
| 28 |
| 32 |
| 36 |
Draw a box plot for this data.
▶️Answer/Explanation
Step 1: Arrange data (already sorted): 12, 15, 18, 20, 24, 26, 28, 32, 36.
Step 2: Find five-number summary:
Min = 12
Q1 = 18 (middle of first 4 values)
Median (Q2) = 24
Q3 = 28 (middle of last 4 values)
Max = 36
Step 3: Draw box from 18 to 28, line at 24, whiskers at 12 and 36.
Example:
The times (in minutes) taken by 11 students to complete a puzzle:
| Times |
|---|
| 6 |
| 8 |
| 9 |
| 10 |
| 12 |
| 13 |
| 14 |
| 15 |
| 18 |
| 20 |
| 22 |
Construct a box plot and comment on the spread.
▶️Answer/Explanation
Step 1: Sorted data: 6, 8, 9, 10, 12, 13, 14, 15, 18, 20, 22.
Step 2: Five-number summary:
Min = 6
Q1 = 9.5 (average of 9 and 10)
Median = 13
Q3 = 17 (average of 15 and 18)
Max = 22
Step 3: Box: 9.5 to 17, line at 13, whiskers at 6 and 22.
Interpretation: Data is slightly skewed to the right (longer upper whisker).
Cumulative Frequency Graphs
Cumulative Frequency Graphs
A cumulative frequency graph shows how the cumulative total of a data set increases as the variable increases. It is useful for estimating medians, quartiles, and percentiles.
Key Features:
- The cumulative frequency is the running total of frequencies up to a certain point.
- The graph is usually drawn as an ogive (a smooth curve or straight lines connecting points).
- The horizontal axis shows the upper class boundaries, and the vertical axis shows cumulative frequency.
Steps to Draw a Cumulative Frequency Graph:
- Create a cumulative frequency table from the given data.
- Plot cumulative frequency against upper class boundary for each class.
- Draw a smooth curve or join with straight lines.
- Use the graph to estimate median, quartiles, and percentiles.
Example:
The table shows the marks of 40 students grouped into intervals:
| Marks | Frequency |
|---|---|
| 0–10 | 3 |
| 10–20 | 5 |
| 20–30 | 10 |
| 30–40 | 12 |
| 40–50 | 10 |
Draw a cumulative frequency graph and estimate the median.
▶️Answer/Explanation
Step: Calculate cumulative frequency:
| Upper Boundary | Cumulative Frequency |
|---|---|
| 10 | 3 |
| 20 | 8 |
| 30 | 18 |
| 40 | 30 |
| 50 | 40 |
Step 2: Plot these points (upper boundary, cumulative frequency) and draw a smooth curve.
Step 3: Median = 50% of 40 = 20th value. Read from the graph at 20 on the cumulative frequency axis → approx 32 marks.
Example:
The weights (in kg) of 50 students are given below:
| Weight (kg) | Frequency |
|---|---|
| 40–50 | 5 |
| 50–60 | 10 |
| 60–70 | 20 |
| 70–80 | 10 |
| 80–90 | 5 |
Draw the cumulative frequency graph and find the interquartile range (IQR).
▶️Answer/Explanation
Step 1: Calculate cumulative frequency:
| Upper Boundary | Cumulative Frequency |
|---|---|
| 50 | 5 |
| 60 | 15 |
| 70 | 35 |
| 80 | 45 |
| 90 | 50 |
Step 2: Plot the graph and read quartiles:
Q1 = 25% of 50 = 12.5th value ≈ 58 kg
Q3 = 75% of 50 = 37.5th value ≈ 72 kg
Step 3: IQR = Q3 − Q1 = 72 − 58 = 14 kg.