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Data Visualization and RepresentationFoundationbox plotcumulative frequencyquartiles

AQA GCSE · Question 11.3 · Data Visualization and Representation

Height, h (m)Cumulative frequency0102030405060708090100051015202530Height, h (m)051015202530

The cumulative frequency diagram below shows information about a sample of 100 trees in a large field. The shortest tree in the field is 1 m in height. The tallest tree in the field is 27 m in height. Use this information and the cumulative frequency diagram to complete a box plot for the trees in the field.

How to approach this question

A box plot requires 5 values: Minimum, Lower Quartile (LQ), Median, Upper Quartile (UQ), and Maximum. 1. **Minimum and Maximum:** These are given in the question as 1m and 27m. 2. **Median (Q2):** This is the value at the 50% mark. Total frequency is 100, so find 50 on the cumulative frequency axis. Go across to the curve and down to the height axis to read the value. (50 -> 12m). 3. **Lower Quartile (Q1):** This is the value at the 25% mark. Find 25 on the cumulative frequency axis. Go across to the curve and down to the height axis. (25 -> 9m). 4. **Upper Quartile (Q3):** This is the value at the 75% mark. Find 75 on the cumulative frequency axis. Go across to the curve and down to the height axis. (75 -> 16m). 5. **Draw the box plot:** - Draw a vertical line at the minimum (1) and maximum (27). These are the whiskers. - Draw a box from the LQ (9) to the UQ (16). - Draw a vertical line inside the box at the median (12). - Connect the box to the whiskers with horizontal lines.

Full Answer

To draw the box plot, we need five key values: 1. **Minimum:** Given as 1 m. 2. **Maximum:** Given as 27 m. 3. **Median (Q2):** The total frequency is 100. The median is at the 50th value. Find 50 on the y-axis of the cumulative frequency diagram, read across to the curve, and then down to the x-axis. This gives a median height of approximately 12 m. 4. **Lower Quartile (Q1):** This is at the (100/4) = 25th value. Find 25 on the y-axis, read across and down. This gives a lower quartile of approximately 9 m. 5. **Upper Quartile (Q3):** This is at the (3*100/4) = 75th value. Find 75 on the y-axis, read across and down. This gives an upper quartile of approximately 16 m. Now we draw the box plot on the provided grid with these five values.

Common mistakes

✗ Reading the values from the cumulative frequency graph inaccurately.\n✗ Mixing up the quartiles and the median.\n✗ Incorrectly constructing the box plot (e.g., box from min to max).

Practice the full AQA GCSE Statistics Foundation Tier Paper 2

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