For my data presentation coursework, I will attempt to prove my hypothesis.
My hypothesis is that European countries are wealthier than African countries.
First of all, I will find the range of both sets of data.
Europe Africa
-55100 -12400
2300 500
Range= 52800 11900
Next I will find the mean for each set of data.
Europe
GDP Tally Freq. Mid Total
0-4999 IIII 4 x 2500 = 10000
5000-9999 IIIIl II 7 x 7500 = 52500
0000-14999 IIIII II 7 x 12500 = 8400
5000-19999 IIIII II 7 x 17500 = 122500
20000-24999 IIIII I 6 x 22500 = 135000
25000-29999 IIIII IIIII I 11 x 27500 = 302500
30000-34999 IIIII 5 x 32500 = 162500
35000-39999 I 1 x 37500 = 37500
40000-44999 0 x 42500 = 0
45000-49999 0 x 47500 = 0
50000-54999 0 x 52500 = 0
55000-59999 I 1 x 57500 = 57500
49 888400
Europe Mean = 888400/49=18130.61
Europe Modal Group = 25000-29999
Africa
GDP Tally Freq. Mid Total
0-999 IIIIl lllll lllll 15 x 500 = 7500
000-1999 lllll lllll lllll llll 19 x 1500 = 28500
2000-2999 Ill 3 x 2500 = 7500
3000-3999 ll 2 x 3500 = 7000
4000-4999 III 3 x 4500 = 13500
5000-5999 Il 2 x 5500 = 11000
6000-6999 Il 2 x 6500 = 13000
...
This is a preview of the whole essay
55000-59999 I 1 x 57500 = 57500
49 888400
Europe Mean = 888400/49=18130.61
Europe Modal Group = 25000-29999
Africa
GDP Tally Freq. Mid Total
0-999 IIIIl lllll lllll 15 x 500 = 7500
000-1999 lllll lllll lllll llll 19 x 1500 = 28500
2000-2999 Ill 3 x 2500 = 7500
3000-3999 ll 2 x 3500 = 7000
4000-4999 III 3 x 4500 = 13500
5000-5999 Il 2 x 5500 = 11000
6000-6999 Il 2 x 6500 = 13000
7000-7999 Il 2 x 7500 = 15000
8000-8999 ll 2 x 8500 = 17000
9000-9999 0 x 9500 = 0
0000-10999 l 1 x 10500 = 10500
1000-11999 I 1 x 11500 = 11500
2000-12999 I 1 x 12500 = 12500
53 154500
Africa Mean =154500/53=2915.09
Africa Modal Group = 1000-1999
I am now going to find the cumulative frequency and use that data to draw a cumulative frequency graph so that I can find the upper and lower quartiles and calculate the interquartile range, I will also find an estimate for the mean.
Europe
GDP Tally Freq. Cum. Freq.
0-4999 IIII 4 4
5000-9999 IIIII II 7 11
0000-14999 IIIII II 7 18
5000-19999 IIIII II 7 25
20000-24999 IIIII I 6 31
25000-29999 IIIII IIIII I 11 42
30000-34999 IIIII 5 47
35000-39999 I 1 48
40000-44999 0 48
45000-49999 0 48
50000-54999 0 48
55000-59999 I 1 49
Europe Median = 20343
Europe Upper quartile = 26809
Europe Lower quartile = 16292
Europe Interquartile range = 26809 - 16292 = 10517
Africa
GDP Tally Freq. Cum. Freq
0-999 IIIIl lllll lllll 15 15
000-1999 lllll lllll lllll llll 19 34
2000-2999 Ill 3 37
3000-3999 ll 2 39
4000-4999 III 3 42
5000-5999 Il 2 44
6000-6999 Il 2 46
7000-7999 Il 2 48
8000-8999 ll 2 50
9000-9999 0 50
0000-10999 l 1 51
1000-11999 I 1 52
2000-12999 I 1 53
Africa Median = 1774
Africa Upper quartile = 4723
Africa Lower quartile = 999
Africa Interquartile range = 4723 - 999 = 3724
I will now find a more accurate median using stem and leaf diagrams.
Europe
Europe Median = 19900
Europe Mode = (this set is quadmodal) 6700, 20000, 22000 and 26800 each occurring twice.
Africa
Africa Median = 1500
Africa Mode = (this set is bimodal) 600 and 800, each occurring four times.
Pie Chart
First of all, I will calculate how many GDP points will be represented by one degree...
888400 1042900
+154500 / 360
042900 2897
Next, I will calculate how many degrees each continent will require...
Europe Africa
888400 154500
/ 2897 / 2897 _
306.66 ____53.33
Before constructing the pie chart, I will add the two above answers to make sure that they add up to 360 degrees, so that I can ensure that my chart is accurate.
306.66
+ 53.33
359.99
This is close enough, as the .01 can be accounted for by the fact that I rounded my answers to avoid calculating all the decimal places.
The pie chart above clearly shows what proportion of their combined wealth each continent owns.
Next, I will construct a box an whisker plot, using figures from both sets of data, because both sets proved to be multimodal, i.e. they had more than one mode, I will use the mid-points of the modal groups acquired from my frequency polygons.
I will use the median gained from the stem and leaf diagrams, as they are more accurate than those from the cumulative frequency curves.
Europe Africa
Median = 19900 Median = 1500
Upper quartile = 26809 Upper quartile = 4723
Lower quartile = 16292 Lower quartile = 999
Highest = 55100 Highest = 12400
Lowest = 2300 Lowest = 500
As well as being generally lower than their like for like European counterparts, the African quantities are also closer together.
The fact that the African quantities are generally lower proves my hypothesis.
To extend this investigation, I am going to state a second hypothesis; life expectancy and GDP are directly linked.
In an attempt to prove this, I will construct a scatter diagram for each continent, plotting GDP (x axis) against life expectancy (y axis). If the correlation is positive, () then my hypothesis will be proved, if the correlation is negative, () then my hypothesis will be disproved.
Europe
N.B. The life expectancy for the Czech Republic was missing, so I have estimated it at 70.
Africa
I have included a line of best fit in my diagram, so that I can estimate life expectancy based on GDP, e.g. if GDP was 5000, I would estmate Life expectancy at 73.
As correlation in both graphs was positive, my hypothesis, that life expectancy is linked to GDP, has been proved.
