Math Investigation Mr. Cockburn
Reflection
Math
Dale Kettern – 8D
Thursday, may 24, 2008.
Types of graphs that could have been used:
A histogram could have been used and the x axis would have the time periods. A line graph could have been used and the x axis could have been the year. (Year 1998, Year 1999 etc.) Good to see trends over time. (Will show) A pie chart (Circle graph) could have been used. Good to show parts as a whole. (Will show) A line plot could have been used. You could have a series of numbers for this. A box and whisker plot could have been used. (Will show) A bar graph could have been used. It is good because you could have the year on the x axis. You could compare them with a bar graph
Table of Values
Year 1998 1999 2000 2001 2002 2003 Amount of births 80 110 115 115 120 130
Dale Kettern 8D
Math Investigation Mr. Cockburn
Graph 1 – Pie Chart (Circle graph)
Births in Peaceful Cove
1998 (12%) 1999 (16%) 2000 (17%) 2001 (17%) 2002 (18%) 2003 (20%)
Reflection
(The Graph was made on Microsoft Excel, yet you can use other similar programs to get a similar result) When you look at this graph it is quite easy to tell which year had the most births, which had the least and so on. The 'key' on the right helps a lot, also due to the fact that it shows the percentage and so you can compare the results as well, not just estimate that in the year 2000 and the year 2001 there were equal amounts of births in Peaceful Cove. It also displays each in a different color, and none of these colors contradict which makes it even easier to understand. This graph would be good if you were trying to compare a specific year to a different year, and to a whole. It would also be good for presentations as it is a more interesting type of graph, yet it is still clear which years had Dale Kettern 8D
Math Investigation Mr. Cockburn which amounts of births. One of the major problems with this graph is that it is not that clear which one is the biggest, and without the key with the percentages it would be hard to compare the different years. This would mean that you would have to literally measure the angles of each in order to compare them. This means that this graph isn't that good because you might not be able to read the percentages that well so you wouldn't be able to understand and compare the graph that well. A line graph or a line plot would have been good for these numbers so that the information would be clearer to read, and with a line graph it would show trends over time. For this data a circle graph is not the best choice, however with the percentages it isn't that bad of a graph to pick. If the numbers varied more it would be even better, however the percentages help a lot in being able to use this graph wisely. I think that the point of the graph is to show trends over time, so a line graph would have been a better choice. Another negative part about this graph is that it does not show the actual number of births, just the percentage out of the total.
Technology
Making this graph by hand would have taken a lot more time than doing it with excel. Also with excel you can just type in the numbers and it will color code everything, give you a 'key' and even the percentages. If you wanted to do it by hand you would have had to add all of the births (670.) You would then have had to put every one of the births as a numerator and then 670 as a denominator and then cross multiply with a variable over 100 to get the percentage. You would then have had to have drawn this graph, and so using modern technology helps a lot and gives you more time. If you did this by hand a calculator would have helped you a lot however you should still have checked your answers, a compass would have made your results much more accurate for this graph. However doing this graph on the computer makes it much more accurate than if you took lots of time drawing it by hand. This makes doing it on the computer much better, because it is faster, looks better and is at the same time much more reliable.
Dale Kettern 8D
Math Investigation Mr. Cockburn
Graph 2 – Line Graph
135 130
125
120
115
110
105
100 1999
2000
2001
2002
2003
Reflection
(The Graph was made on Microsoft Excel, yet you can use other similar programs to get a similar result) This line graph is very good because of many reasons. The first reason is that it clearly shows the amount of births and in what year they occurred. The graph is also good because it is easy to see trends over time. This makes it easy to compare the amounts of births between the years much easier. However it isn't such a good graph because it doesn't show the percentage of all those years together, which would make it easy to see in which years the percentage of births was high. However I think that showing trends over time is more important than this, and so this is not such a decisive factor. However I think that the pie chart looks better and it is easier to see estimates of the amounts of births in which year, yet altogether this graph is better. I think this due to the fact that many people like to easily see how the numbers increased, in which case this graph is much simpler.
Technology
Making this graph with Microsoft Excel is faster and easier than drawing this graph by hand. This is due to the fact that with Excel all you have to do is put in the numbers, check some boxes and then the graph is done. If you did this graph by hand you would have to measure the lines accurately, write all the numbers and then draw the lines. The computer makes the lines perfect, and so the graph is accurate. If you however drew this graph by hand it would probably not be perfectly to scale, the lines and numbers would be a bit of etc. This makes it much easier to do this on the computer, and at the same time more reliable.
Dale Kettern 8D
Math Investigation Mr. Cockburn
Reflection
The box and whisker plot is a summary of the data for the amount of births. What is displayed in the Dale Kettern 8D
Math Investigation Mr. Cockburn box and whisker plot is basically a rough idea about how many births were given, and the five number summaries. The five number summary is good because you can summarize large bits of data in order to give the reader something that is easy to read. The five number summaries show the smallest number so that they (Person reading this) know that this is the lowest amount the whiskers can stretch to. They can then look at the five numbers summery and they will see the lower quartile, which is equal to the 25% mark of the date. They can then look at the median, which is the 50% mark of all the data. If they then look at the upper quartile they will see the upper quartile which is the 75% mark of the data. The person will then be able to see the maximum, and so they will know the highest number that the whiskers can stretch to. Outliers are shown by asterisks. Outliers are piece of data that are abnormally high or low numbers compared to the rest, for example if most of the data is in the 50's and then there is one number that is at 95 then there will defiantly be at least one outlier, 95. The main advantage of the box and whisker plot is that it shows the important numbers that somebody might want to be able to find easily. This saves time if you are just looking for a few important pieces of information on the data. Another example of the box and whisker plot is that it can not get complicated; even if there are lots of numbers in the data you can still easily tell the important stuff. A disadvantage of the box and whisker plot is the fact that there are only a few numbers, which is good if you only want a summery of all the data but if you want to be able to see it clearly it is not that good. Altogether a box and whisker plot is very good because the reader can see the important parts of the data really easily. The reader knows the data because he can see the data really clearly as it is organized well. The major problem with the box and whisker plot is that the reader might not understand in which years these births occurred, and so he cannot easily compare trends over time. One reason why the box and whisker plot is not that good to use is due to the fact that you cannot tell all of the numbers easily, and if somebody is looking for the information displayed like this it is bad. Also box and whisker plots are usually used to summarize a lot of data, with lots of data. With little data there is no real need for a box and whisker plot. You wouldn't really need to summarize the data like this since there are only 6 pieces of data.
Technology
A good method of making the box and whisker plot is using a creator on the internet. This is good because of the fact that the internet can also give you the five number range, which takes away a lot of time. There are websites on the internet, and there are also most likely mathematic programs that can help you do this. I saw a website where there was basic data, you would then just press clear and you could enter your own information. The website would even give you the five number range with all of the numbers filed in. On the internet you can enter lots of numbers; if you had the amount of numbers you can put in there it would take ages to work them out. Another good thing is that it automatically shows the actual box and whisker plot. These types of programs are very good for this and take away a lot of valuable time. You can then know what the box and whisker plot should look like. You can also use a calculator to work out the five number summaries, yet doing it on the internet is much faster.
Dale Kettern 8D
Dale Kettern 8D