Setareh Gerashi
8D
Saturday, May 24, 2008.
Math Reflection
There are many types of graphs could be used to display the data for “Births in Peace Cove, 1998-2003”. The graph that has been shown above is a bar graph and it is showing the number of births from the years 1998 till 2003 in a place called “The Peaceful Cove”. The bar graph is a quite good choice of graph for this data because you have the year on the x-axis and the number of births going up in tens in the y-axis. You can easily compare the differences of births from year to year. You can clearly see which one had the most amount of births, and which had the least. So comparing bar graphs is pretty easy since the higher the bar from the other, the more amounts of births it has. You can draw the data displayed in the bar graph using many other types of graphs. They include using circle graphs, line graphs, line plot, and box-andwhisker plot. You could use all these graphs because the data displayed on the bar line tells us the exact years and shows the data very clearly even though it is going up in tens so it is easy to figure out the data. All the graphs listed have different purposes. Bar graphs display the frequency of categories, line graphs show trends over time, circle graphs show categories a part of a whole, histograms and line plots show the frequency distribution of measurement data and box-and-whisker plot summarize the distribution of measurement data. You can use all these graphs to plot the points of the data below which I figured out from the bar graph since it has been graphed very clearly stating all the data clearly. You could draw a circle graph by adding up all the births from the years 1998 to 2003 and then finding the percent by for example putting 80 births (1998) over the total sum of all the births from 1998-2003, which is 670, and then multiplying 80/670 by 100. Then your answer will be approximately 12 and that is the percentage. You do this for the other years as well and when you add them all up, you will get 100% and these percentage of a part of a whole for the years 1998-2003. To do line graph, you make the x-axis the years (1998-2003) and you make the y-axis the number of births going constantly up in 10s. You can also make the xaxis go up in 5s or 20s. You plot the births on the graph for each year and then you connect the plots by using a straight ruler. This can easily show the trends over time and this is the whole purpose of this graph. You can easily determine the patterns by looking at it and comparing the numbers. For the x-axis, you must make sure you put the break symbol since you are starting from 1998 which otherwise means you should've started at an earlier year. To do a Line Plot, you could have the series of number 80, 85, 90, 95, 100, 105, 110, 115 120, 125 and 130. You could then put an „x‟ on the numbers according to the number of births from the years 1998-2003. For this graph, you can only have one variable, so you the years 1998-2003 have to be the heading of the graph. Also this graph is doable, it is not a very good choice and I recommend
Setareh Gerashi
8D
Saturday, May 24, 2008.
you shouldn‟t use it for this type of graph since it will not show information and data well. This graph can also not be used is because the purpose of using this is to show the frequency of data and it wouldn‟t work with our data since we had different years and different amount of births for the years. A box-and-whisker plot can be done as well. You can use the six pieces of data available from the bar graph and use it in the five number summary. The five number summary includes the minimum, the lower quartile, the median, the upper quartile, and the maximum. You must find all five of the number summary from the six pieces of data and then you can plot them on a consistent number line. Year 1998 1999 2000 2001 2002 2003 Births in Peaceful Cove 80 110 115 115 120 130
The First Graph: Circle Graph
Births in Peaceful Cove, 1998-2003
2003 20%
1998 12% 1999 16%
2002 18% 2000 17%
2001 17%
Working Out: Total of births = 670 (from 1998 to 2003) 1998: 80/570 x 100 = (approx) 12 % Then to convert this to degrees on the circle, this is what you do: 12/100 x 360 = 43.2 degrees
Setareh Gerashi
8D
Saturday, May 24, 2008.
Reflection: This is circle graph it shows the percentage and categories as a whole. In this circle graph, it shows the amount of birth each year starting with 1998-2003 as a whole and you can see the percentages written beside the sections of the years. This is very helpful since the percentages help you compare them with each other and this way you can figure out which year had more births than the other. The circle graph is very colouful and the colours are all different and you can clearly see each year and sections. This makes the reader‟s life easier by distinguishing each section and knowing what the years are clearly. On big disadvantage of this graph with this particular data is that since they are all a bit similar in the number of births, or a bit close in number, you cannot really compare which one is bigger than the other by just looking at the graph. The only obvious one is that the blue section, year 1998, shows that it is the smallest section which means that the number of births in this year was the least. However, if you look at the other sections, they all look similar in size, and other than looking at the percentages listed, the only other way to determine to sizes of the sections and which is larger and has more births (other the smallest sections which is the blue) is to either look at the table of data or to actually come and measure the degrees of the sections using a protractor. This can show you the degrees of the sections and the whole circle being 360 degrees since circles are always 360 degrees and straight lines are 180 degrees, therefore 180 degrees multiplied by 2 gives you 360 degrees (a whole circle). How a circle graph would be better is that if it was used with data which were numbers very much further apart, then you would actually visually see the obvious changes and how one section would be bigger and obviously with a larger percentage, not close to each other at all. This would be very easy to spot the larger numbers and which one is bigger and smaller than the other. This graph also does not show the data and how many births there are in a year which is very unhelpful, especially if you were trying to determine data from the graph which is almost impossible. This means that circle graphs only show percentage without the numbers of birth so someone could guess the number of births which is not exactly what people are suppose to do when they read a graph. The graph is supposed to tell them the data, not them guessing and being puzzled. Also this graph does not show you trends and patterns over time since the data is actually for births happening over time. This is a disadvantage because then the reader cannot determine whether the births have increased rapidly or slowly. Even though the percentages are listed, the aren‟t as effective as a line graph which the steepness determines how rapidly or how slowly the number of births have changed from a year to the next. A line graph shows in total how much the number of births have changed from the year 1998 to the year 2003. The reader can also determine in what years the births have been the most increased and in what years haven't the births numbers changed, or increase just a little bit. So in this case and situation, a line graph would be much more appropriate if used with the data we have with is amount (of births) over time. This way patterns and trends will be much more obvious and easy to stop. This will be much easier for the reader, especially if the
Setareh Gerashi
8D
Saturday, May 24, 2008.
reader is not so good with graphs and won't spot many differences in circle graphs than they will easily on line graphs. I don‟t think there is much a reader can get from this type of graph since all you can see are the percentages of the births from the years 1998-2003 and the most important part which is the data is not even shown which is pointless because the reader cannot get much from just percentages. The reader has no clue how many births there are in Peaceful Cove. Some might guess 10, 000 for 1998, and some might guess 500 births when in truth its less. It is impossible for the reader to figure out from percentages, except if you actually put a table of data or you told the reader the total amount of births there were from 1998-2003, which is 670. Then this way they could find how many births 12% of 670, and how many births 20% is and so on with the other percentages shown on the circle graph. Technology for Circle Graphs There are many ways you could use technology for helping you out for drawing and calculation circle graphs. You could use the old fashioned way, which is to calculate the data and draw it by hand using a calculator, pencil and a protractor. For this type of data, you must first add all the number of births from the year 1998 till the year 2003 and that becomes you total and the „whole‟ you are going to use for the circle graph. Then you take the number of births from 1998 and you put it over 670 (the total number of births 1998-2003), and then you multiply it by 100 to get a percentage. So 80/670 x 100 = 11 63/67 which is the same as 11.94029851 %. This is approximately 12%. You do the same for the year 1999. You put 110 over 670 and then multiply it by 100. 110/670 x 100 = 16 28/67 which is the same as 16.41791045 %. When you then calculate all the percentages of all the years, then they must add up to 100%, otherwise your calculations would be wrong. You could easily do this on the calculator for you would get all the calculations and percentages correctly and very fast rather than working out and multiplying fractions. After working out the percentages using a calculator, you could use a geometric instrument called a protractor to draw the circle chart. So you first draw a circle making it a normal size, not too small or you won't see it well. You then calculate the perecentages to degrees out of 360. This time what you have to do is have the percentages over 100 and the multiply them by 360. So for 1998, you put 12/100 and you multiply by 360, and this equals to 36 degrees. So you calculate 36 degrees with a protractor and then draw it on the 360 degree circle. You then calculate all the other percentages to degrees through the same process and then at the end when you add all the degrees, they should add up to 360 degrees in total. Then you use a protractor to draw all the degrees for the years. You then have to label them after drawing each section (year) on the circle. Another way you could do this is by using programs on the computer. On program is a Microsoft Office program called “Excel”. Here you have a table where you just have to enter the data and put titles for the x and y axis, and then
Setareh Gerashi
8D
Saturday, May 24, 2008.
create a graph by highlighting the data and then clicking on the picture of a bar graph and its called „Chart Wizard‟. Or you can click on the „Insert‟ button on the top and then click on „Chart…” W hen you clicked on it, you click on the pie for the chart type and then it will take you through a process of creating it. You can also click preview before creating it so you can see how it looks and whether you like it or not. You can always changed the colours of the sections to other colours you like. You can also have a small chart indicating what each section means (which in this case would be the years), but the graph I've done already has the years labeled beside it, so you won't need a small chart indicating what the sections stand for. The last way I know which you can use to draw a circle graph is using a graph creator on the internet. There are many websites in which you can use to make a circle graph by writing down the variable names and then the actual data you want them to graph. A good and simple website is http://nces.ed.gov/nceskids/createagraph/default.aspx. This is such a simple and straight forward website that kids can easily use it. It has been designed for kids anyway but teenagers and teachers can use them to create simple and yet effective graphs that is very easy to read and understand. This website also has many other types of graphs which you can use to create. The Second Graph: Box-and-Whiskers Data from least to highest : 80, 110, 115, 115, 120, 130 Minimum = 80 Lower Quartile = 110 Median = 115 Upper Quartile = 120 Maximum = 130 IQR = UQ – LQ = 120 – 110 = 10 IQR x 1.5 = 10 x 1.5 = 15
This is a box-and-whisker plot and it shows the summary of the data for the amount of births from 1998-2003. What is displayed in this box-and-whisker plot that tells the reader is a rough idea about how many births were given and the five number summary. The five number summary is a very good way of summarizing the data and giving the reader a rough idea about the data. Firstly it tells the reader the minimum data available so that they know what the lowest piece of numeric data is and what doesn‟t get any lower than that. Then they will
Setareh Gerashi
8D
Saturday, May 24, 2008.
know the lower quartile which equals to the 25% mark of all the data. Then they will know the median which is simply the 50% mark of all the data. Then there is the upper quartile which indicates the 75% mark of all the data. Lastly, they will know the maximum and they maximum is the highest piece of numeric data which tells us no other data exceeds the maximum. This plot also shows you that there is an outlier from the asterisks. Outliers are pieces of data that are „outcasts‟ to the majority of the data. In simpler words, an outlier is a number is a set of data that is much larger or smaller than most of the numbers in the number set. A clear example is that from [3,5,4,4,6,2,25,] the outlier is 25 and this is because 25 is way larger than the rest. The main advantage of the box-andwhisker plot is that it is not cluttered by showing all the data values. It highlights only a few important features of the data which saves time rather than going through a graph which a lot of data and get getting confused. Therefore, the boxand-whisker plot makes it easier to focus attention on the median, extremes, and quartiles and comparisons among them and this is what graphs are really for. Another advantage of the box-and-whisker plot is that it does not become more complicated with more data values unlike circle graphs might get crowded. A disadvantage of the box-and-whisker plot occurs when there are only a few data values. The readers get so much from this type of graph since you can see the highlights of the data and what is the most important. This can then tell them what the lowest and highest piece of numeric data is which then makes the remaining pieces of data be between the minimum and maximum. The reader knows the data, unlike the reader who wouldn‟t notice the data for the circle, because you can see from the number line the number of births summary. What the reader might not get from this graph is that the fact of which years did you have which amount of births. It is not life a line graph which displays all the changes which might be happening between the pieces of data. A reason why this graph shouldn‟t have been used is because this is usually used to summarize lots of data to keep it simple and easy for the reader to look at and understand. But we only have six pieces of data which isn‟t much that absolutely requires the boxand-whisker plot since you wouldn‟t need to summarize the results since there is only about six pieces of numeric data. There are many ways of plotting the box-and-whisker plots and data. One way is using the old fashioned way which is simply to draw it on graph paper. You first arrange the data from the least to the greatest. Then find the median of the data. The median is found by being the middle number when the numbers are arranged from least to greatest. If you have an even number of numbers, the median is the average of the middle two numbers. Then you find the lower quartile which is found by finding the median of the numbers that are to the left of the median. You then find the upper quartile by finding the median of the number to the right of the median. You then draw the number line that contains all the values that is in the data. You then place a dot above the numbers that represent you minimum value, the lower quartile, the median, the upper quartile and the
Setareh Gerashi
8D
Saturday, May 24, 2008.
maximum value. Then draw a rectangle that has boundaries of the two quartiles. Then, draw a line through the rectangle at the median. You now have a box. Draw the line from the lower quartile to the minimum value and another line from the upper quartile to the maximum value. These two lines are called the whiskers. Technology for Box-and-Whisker A good method of doing the box and whiskers is by going online and searching the box-and-whisker creator. A good website I found is http://nlvm.usu.edu/en/nav/frames_asid_200_g_4_t_5.html?open=ins tructions&fr om=applets/controller/query/query.htm?qt=box+plot . This website is like a mini version of an online program but it is very easy to use. They have a table which you could press „clear‟ and then enter your own data for. The table that they have allows you to put as much as 100 data numbers and more as you like. The cool thing is that it automatically shows you the box-and-whisker plot and all the five number summary at the bottom. For the graph, it also shows you the timeline they have used for the graph. This is a very easy way of using internet and technology to create a box-and-whisker plot in no time. You can also download a free trial version onto your desktop if you would feel more comfortable working on the box and whisker offline. The best thing is that this program is feel and is available for every to use which is very good. This website is straight forward and easy to figure out and use. Also the box that they create is very clear to the reader which is also very good. Other obvious tools that can be used is a calculator. You can use a calculator to figure out the five number summary or to find the median, LQ or the LQ if the number of your number data is even. What you do is you take the middle two numbers, add them together, and then divide them by two. You do the same if you also have even number of numbers on the left and right side of the median.