Edexcel IAL S1 Representation of Data Questions
Histograms (frequency density), stem-and-leaf, box plots, cumulative frequency, outliers, skewness; comparing distributions.
- S1 · Statistics 1
- Calculator allowed
- 35 practice questions
What the questions test
The 35 S1 representation of data practice questions cover:
Worked example 1
The data in a histogram is grouped into classes. A bar representing the class $100 \le x < 150$ has a width of $2.5\text{ cm}$ and a height of $4\text{ cm}$. The total area of all bars in the histogram is $90\text{ cm}^2$. If the bar for $100 \le x < 150$ represents a frequency of $20$, calculate the total frequency of the entire data set.
Mark scheme
- M1 for calculating the area of the specified bar: $2.5 \times 4 = 10\text{ cm}^2$.
- M1 for establishing the relationship between area and frequency: $10\text{ cm}^2$ represents a frequency of $20$.
- A1 for calculating the scale factor: $1\text{ cm}^2$ represents $2$ items (since $20 / 10 = 2$).
- M1 for using the total area to find total frequency: $90\text{ cm}^2 \times 2$.
- A1 for the final answer: $180$ items.
Worked example 2
A histogram is drawn. The class $0 \le x < 20$ has frequency $10$, and the class $20 \le x < 30$ has frequency $30$. If the height of the bar for the first class is $2\text{ cm}$, find the height of the bar for the second class, assuming the width of the bars is proportional to the class width.
Mark scheme
- M1 for stating the class widths: $20$ and $10$.
- M1 for establishing the width ratio: if class width $20$ has a certain drawn width, class width $10$ has half that drawn width. Let drawn width of first bar be $2w$, then second bar is $w$.
- M1 for using Area $\propto$ Frequency for the first bar: Area $= 2w \times 2 = 4w$. So $4w$ represents frequency $10$, meaning $w$ represents frequency $2.5$.
- M1 for applying to the second bar: Area $= w \times h$. Frequency $= 30$. So $w \times h$ represents $30$. Since $w$ represents $2.5$, Area must be $12w$.
- A1 for solving for height: $w \times h = 12w \implies h = 12\text{ cm}$.
FAQ
What representation of data is in Edexcel IAL S1?
Histograms (frequency density), stem-and-leaf, box plots, cumulative frequency, outliers, skewness; comparing distributions.
Is S1 a calculator paper?
Yes, a calculator is allowed in S1, but method marks are only given for working you write down.
How are S1 representation of data questions marked?
With M marks for a correct method, A marks for accurate answers that depend on the M mark before them, and B marks for independent results, as in the worked examples on this page.