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# Charting Success

##### Stage: 3 and 4 Challenge Level:

Nick from Neutral Bay Public School in Australia commented on the first diagram:

Scatter plot showing Federer's first serve landing points:

Federer scored the most aces on the right side near the centre. To return the serve, you should stand a little more than a quarter of the base line from the ends. It would be useful if the plot showed where Federer stood for each serve. The chance of Federer scoring an ace was $\frac{13}{43}$ (or $30.2\%$).

The Pythagoreans from All Saints School in Dagenham analysed and commented on two of the diagrams:

Scatter plot showing Federer's first serve landing points:

The Tennis diagram shows where the ball bounced, you can see that the tennis player did well but it doesn't show the speed the served ball was travelling at. The bounced balls could also be labeled better (e.g make the graph bigger and maybe add a few colours to the bounces that were close to each other).

It could also show serves that went out, because we don't know what percentage of serves were out.

League positions of teams in a football league during a season:

We do not like this graph! It is all over the place. The colours of the lines are confusing: when the lines intersect you can't see where they carry on because the colours are too similar. There is no key so we don't know which colour represents which team. There is too much information on the graph and so it is not clear. To improve it they could have separated the graph into a top half of the table and the bottom half, or a top six (European places) and bottom three (relegation zone).

Hattie and Daizee from Gisborne Intermediate in New Zealand shared their thoughts on four of the diagrams:

Scatter plot showing Federer's first serve landing points:

Federer scored the most aces in the middle. So the best place to return the serve would also be in the middle. It would help to know where Federer was standing for each serve.

"Heat map" showing the position of players in one team in a football match:

The team was playing up the pitch, We think the team spent more time attacking as much of the action of the game took place at the upper end of the pitch. The team's formation seemed to be spread out in the lower half of the pitch and in groups in the upper half. The team's strategy seemed to be to work on their defence, while we think the opposing team focused on spreading out.

Finishing scores of the top ten athletes in Olympic heptathlon:

The 4th to 10th positions tend to be grouped together, whereas 1st to 3rd tend to be quite separate. The highest performing winner was in 1988, while the closest competetition was in 2008. To win a medal in this event, we think you would need to get a score of about 6800.

Shots on and off target for one team in a football match:

We felt that the attacking team wasn't very accurate and the defending team was moderately effective at stopping goals since there were about as many goals as there were blocked shots. If we were attacking, we would aim for the left side of the goal because most of the goals were scored on that side. We feel that the chance of scoring a goal decreases as the distance from the goal increases because defenders have more time to intercept the ball.