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AQA GCSE · Question 12.1 · Statistics
Liz records the distance of some runs and the time each run takes. The table and scatter graph show some of the information.
Complete the graph by adding the missing label and plotting the two missing points.
Liz records the distance of some runs and the time each run takes. The table and scatter graph show some of the information.
Complete the graph by adding the missing label and plotting the two missing points.
How to approach this question
1. **Find the missing label:** Look at the table. The horizontal axis (x-axis) corresponds to the top row of the table. The label should be "Distance (km)".
2. **Identify the missing points:** Compare the data in the table with the points already plotted on the graph. The points for (3, 14), (4, 17), (5.5, 22), (6, 23), (6.5, 26), and (7, 31) are already there. The missing points are (8, 38) and (8.5, 42).
3. **Plot the first missing point (8, 38):** Find 8 on the horizontal axis and 38 on the vertical axis. Mark the point where these two lines would intersect.
4. **Plot the second missing point (8.5, 42):** Find 8.5 (halfway between 8 and 9) on the horizontal axis and 42 on the vertical axis. Mark the point where these two lines would intersect.
Full Answer
The missing label on the x-axis is "Distance (km)".
The two missing points to be plotted are (8, 38) and (8.5, 42).
See the completed graph:
<svg width="700" height="700" viewBox="0 0 450 450" xmlns="http://www.w3.org/2000/svg">
<style>
.label { font: bold 12px sans-serif; }
.axis-label { font: 10px sans-serif; }
.title { font: bold 14px sans-serif; text-anchor: middle; }
.point { fill: black; }
.new-point { fill: red; }
</style>
<text x="225" y="20" class="title">Running distances and time taken</text>
<!-- Y Axis -->
<line x1="50" y1="50" x2="50" y2="400" stroke="black"/>
<text x="15" y="225" class="axis-label" transform="rotate(-90, 15, 225)">Time (min)</text>
<g class="axis-label" text-anchor="end">
<text x="45" y="405">0</text>
<text x="45" y="365">5</text><line x1="45" y1="360" x2="50" y2="360" stroke="black"/>
<text x="45" y="325">10</text><line x1="45" y1="320" x2="50" y2="320" stroke="black"/>
<text x="45" y="285">15</text><line x1="45" y1="280" x2="50" y2="280" stroke="black"/>
<text x="45" y="245">20</text><line x1="45" y1="240" x2="50" y2="240" stroke="black"/>
<text x="45" y="205">25</text><line x1="45" y1="200" x2="50" y2="200" stroke="black"/>
<text x="45" y="165">30</text><line x1="45" y1="160" x2="50" y2="160" stroke="black"/>
<text x="45" y="125">35</text><line x1="45" y1="120" x2="50" y2="120" stroke="black"/>
<text x="45" y="85">40</text><line x1="45" y1="80" x2="50" y2="80" stroke="black"/>
<text x="45" y="45">45</text><line x1="45" y1="40" x2="50" y2="40" stroke="black"/>
</g>
<!-- X Axis -->
<line x1="50" y1="400" x2="430" y2="400" stroke="black"/>
<polyline points="425,395 430,400 425,405" fill="none" stroke="black"/>
<text x="240" y="435" class="axis-label" fill="blue" font-weight="bold">Distance (km)</text>
<g class="axis-label" text-anchor="middle">
<text x="90" y="415">1</text><line x1="90" y1="400" x2="90" y2="405" stroke="black"/>
<text x="130" y="415">2</text><line x1="130" y1="400" x2="130" y2="405" stroke="black"/>
<text x="170" y="415">3</text><line x1="170" y1="400" x2="170" y2="405" stroke="black"/>
<text x="210" y="415">4</text><line x1="210" y1="400" x2="210" y2="405" stroke="black"/>
<text x="250" y="415">5</text><line x1="250" y1="400" x2="250" y2="405" stroke="black"/>
<text x="290" y="415">6</text><line x1="290" y1="400" x2="290" y2="405" stroke="black"/>
<text x="330" y="415">7</text><line x1="330" y1="400" x2="330" y2="405" stroke="black"/>
<text x="370" y="415">8</text><line x1="370" y1="400" x2="370" y2="405" stroke="black"/>
<text x="410" y="415">9</text><line x1="410" y1="400" x2="410" y2="405" stroke="black"/>
</g>
<!-- Grid lines -->
<g stroke="lightgrey" stroke-width="0.5">
<path d="M 50 360 H 420 M 50 320 H 420 M 50 280 H 420 M 50 240 H 420 M 50 200 H 420 M 50 160 H 420 M 50 120 H 420 M 50 80 H 420 M 50 40 H 420"/>
<path d="M 90 50 V 400 M 130 50 V 400 M 170 50 V 400 M 210 50 V 400 M 250 50 V 400 M 290 50 V 400 M 330 50 V 400 M 370 50 V 400 M 410 50 V 400"/>
</g>
<!-- Data Points -->
<text x="170" y="280" font-size="20" class="point">x</text> <!-- (3, 14) -> approx 15 -->
<text x="210" y="264" font-size="20" class="point">x</text> <!-- (4, 17) -->
<text x="270" y="224" font-size="20" class="point">x</text> <!-- (5.5, 22) -->
<text x="290" y="216" font-size="20" class="point">x</text> <!-- (6, 23) -->
<text x="310" y="192" font-size="20" class="point">x</text> <!-- (6.5, 26) -->
<text x="330" y="152" font-size="20" class="point">x</text> <!-- (7, 31) -->
<text x="370" y="96" font-size="20" class="new-point">x</text> <!-- (8, 38) -->
<text x="390" y="64" font-size="20" class="new-point">x</text> <!-- (8.5, 42) -->
</svg>
**Part 1: Adding the missing label**
The vertical axis is labelled "Time (min)", which corresponds to the bottom row of the table. Therefore, the horizontal axis must correspond to the top row of the table, which is "Distance (km)".
**Part 2: Plotting the missing points**
We need to check which data pairs from the table are not on the graph.
- (3, 14) - Plotted
- (4, 17) - Plotted
- (5.5, 22) - Plotted
- (6, 23) - Plotted
- (6.5, 26) - Plotted
- (7, 31) - Plotted
- **(8, 38) - Missing**
- **(8.5, 42) - Missing**
We need to plot these two points:
- **To plot (8, 38):** Go along the horizontal axis to 8, then go up to 38 on the vertical axis. Place a cross at this position.
- **To plot (8.5, 42):** Go along the horizontal axis to 8.5 (which is halfway between 8 and 9), then go up to 42 on the vertical axis. Place a cross at this position.
Common mistakes
✗ Plotting the coordinates the wrong way around (e.g., plotting (38, 8) instead of (8, 38)).
✗ Misreading the scales on the axes.
✗ Forgetting to add the label for the x-axis.
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