∑X2 8499915
n 811
10 480.78 – m2
➔ 10 480.78 – 10 314.43
S2= 166.35
➔ √166.35= 12.90 (2dp)
➔ 13 (2sf)
The standard deviation of the IQ of the students in Key Stage 3 is 13. From this I can gather that the dispersion across both sides of the mean (101.56) is low. This shows that generally the Key Stage 3 students are quite intelligent. However this means that the lowest average IQ is 88.56 and the highest average is 114.56.
Because the standard deviation is 13 and the mean is 101.56, the standard deviation shows that the data is not widespread across the mean, which in turn shows that there are no extreme values. The presence of extreme values would prove that some students have a very high intelligence quotient while others may not have an IQ that high. This would in turn; mean that the group as a whole does not have a very high intelligence quotient.
I will now be measuring the dispersion of the IQ from the mean of the Key Stage 4 students.
I will again be using the
∑X2
n
The mean is 99.97.
X stands for the IQ of all the students in Key Stage 4.
∑X2 3640233 10460.44
n 348
10460.44 – m2
➔ 10 460.44 – 9 994
S2= 466.44
➔ √466.44= 21.6
➔ 22 (2sf)
The standard deviation of the IQ of the students in Key Stage 4 is 22. From this I can gather that the dispersion across both sides of the mean (99.97) is quite widespread. This shows that generally the Key Stage 4 students are not so intelligent. However this means that the lowest average IQ is 77.97 and the highest average is 121.97.
Because the standard deviation is 22 and the mean is 99.97, the standard deviation shows that the data is widespread across the mean, which in turn shows that there are extreme values. The presence of extreme values proves that some students have a very high intelligence quotient while others may not have an IQ that high. This would in turn; mean that the group as a whole does not have a very high intelligence quotient.
I will now be measuring the dispersion of the IQ of the blonde haired and blue eyed students in Key Stage 3; from the mean IQ of Key Stage 3.
Blonde-haired, blue-eyed students (KS3)
I will again be using the equation
∑X2
n
The mean is 101.56.
∑X2 12666525 10467.98
n 121
10467.98 – m2
➔ 10467.98 – 10314.43
S2= 153.55
➔√153.55 = 12.39
➔ 12 (2sf)
Non blonde-haired, blue-eyed students (KS3)
Equation:
∑X2
n
The mean is 101.56
∑X2 7287913 10562.19
n 690
10562.19 – m2
➔ 10562.19 – 10314.43
S2= 247.76
➔ √247.76= 15.74
➔ 16 (2sf)
Comparing the two standard deviations that I have worked out, 12 (KS3 blonde/blue) and 16 (KS3 non blonde/blue), I have found that the blonde-haired, blue-eyed students of Key Stage 3 have a lower deviation than the students with different phenotypes. This indicates that as a group they have a higher intelligence quotient than the non blonde-haired, blue-eyed students in the same Key Stage.
A lower deviation shows that all the students have similar intelligence and there are no extreme values. The presence of extreme values would prove that some students have a very high intelligence quotient while others may not have an IQ that high. This would in turn; mean that the group as a whole does not have a very high intelligence quotient.
I will now be measuring the dispersion of the IQ of the blonde haired and blue eyed students in Key Stage 4; from the mean IQ of Key Stage 4. I will do the same to the non blonde-haired, blue-eyed students in Key Stage 4. I will compare the two results and then determine which group has a higher intelligence quotient as a whole.
Blonde-haired, blue-eyed students (KS4)
I will use the formula:
∑X2
n
The mean is 99.97
∑X2 569675 10357.72
n 55
10357.72 – m2
➔ 10357.72 – 9994
S2= 363.72
➔ √363.72 = 19.07
➔ 19 (2sf)
Non blonde-haired, blue-eyed students (KS4)
I will use the formula:
∑X2
n
The mean is 99.97
∑X2 2994982 10221.78
n 293
10221.78 – m2
➔ 10221.78 – 9994
S2= 227.78
➔ √227.78 = 15.09
➔ 15 (2sf)
Comparing the two standard deviations that I have worked out, 19 (KS4 blonde/blue) and 15 (KS4 non blonde/blue), I have found that the blonde-haired, blue-eyed students of Key Stage 4 have a higher deviation than the students with different phenotypes. This indicates that as a group they have a lower intelligence quotient than the non blonde-haired, blue-eyed students in the same Key Stage.
A higher deviation shows that all the students have dissimilar intelligence and there are extreme values. The presence of extreme values would prove that some students have a very high intelligence quotient while others may not have an IQ that high. This would in turn; mean that the group as a whole does not have a very high intelligence quotient.
Range: 40
Range: 16
From the two scatter graphs, I can see different ranges for both the samples. A lower range shows that the data is less spread out. This also means that the as a group the non blonde-haired, blue-eyed students of Key Stage 3 have a higher intelligence quotient. A higher average shows that there are some extreme values. For example here, the highest value was 111 and the lowest value was 71. These extreme values point out that there are some students who are very intelligent, whereas there are some students who are not so clever. It also points out the fact that as a group, the blonde-haired, blue-eyed students of Key Stage 3 have a lower intelligence quotient than their counterparts with a different phenotype.
Range: 35
Range: 28
From the two scatter graphs, I can see different ranges for both the samples. A lower range shows that the data is less spread out. This also means that the as a group the non blonde-haired, blue-eyed students of Key Stage 4 have a higher intelligence quotient. A higher range shows that there are some extreme values. For example in the “IQ of blonde-haired, blue-eyed students in KS4”, the highest value was 116 and the lowest value was 81. These extreme values point out that there are some students who are very intelligent, whereas there are some students who are not so clever. It also points out the fact that as a group, the blonde-haired, blue-eyed students of Key Stage 3 have a lower intelligence quotient than their counterparts with a different phenotype.
However, this group is not the only one to have such extreme values. The “IQ of non blonde-haired, blue-eyed students in KS4” graph shows that this group also has some extreme values. In this group there are some students who are very intelligent (IQ 112) and some students who aren’t so intelligent (IQ 94). But as group, and having a lower range of IQ, they are generally more intelligent than the blonde-haired, blue-eyed students in Key Stage 4.
I have decided that to further investigate the opinion “Blonde haired, blue eyed people are better than others” and to obtain more accurate results, I will have to investigate the truth of this statement in the separate year groups.
First, to obtain my sample, I will carry out stratified sampling to determine the number of students I will choose from each year and each of the phenotypes that I am investigating into. After that I will use random sampling to determine who to choose.
Stratified Sampling
Year 7: 282 / 813= 0.34686346863468634686346863468635
0.34686346863468634686346863468635 x 81= 28 students
From here I will have to take a number of pupils from the blonde-haired, blue-eyed students and the non blonde-haired, blue-eyed students to make sure that I have unbiased readings.
Year 7 (blonde-haired, blue-eyed students):
35 / 283= 0.12367491166077738515901060070671
0.12367491166077738515901060070671 x 28= 3 students
Year 7 (non blonde-haired, blue-eyed students):
248 / 283= 0.87632508833922261484098939929329
0.87632508833922261484098939929329 x 28= 25 students
From these calculations I can see that if I were to draw a graph, then I would have too many points for the non blonde-haired, blue-eyed students and very little for the blonde-haired, blue-eyed students. I have now decided to increase the sample for the blonde-haired, blue-eyed students to 70%. The reason as to why I have chosen this particular percentage is that I thought it would be the closest number to the non blonde-haired, blue-eyed students. The reason as to why I had thought this was that if 10% = 3, then the closest number to 25 would be multiplying it by 0.70 (70%). Therefore it would be 3 x 7= 27.
Year 7 (blonde-haired, blue-eyed students):
35 / 283= 0.12367491166077738515901060070671
0.12367491166077738515901060070671 x 212.25= 26 students
Now as you can see, the number of students that I will display for the blonde-haired, blue-eyed students is a much larger number and I will now be able to draw a meaningful conclusion from any graphs that I may show.
Year 8 (blonde-haired, blue-eyed students):
45 / 272= 0.16544117647058823529411764705882
0.16544117647058823529411764705882 x 27= 4 students
Year 8 (non blonde-haired, blue-eyed students):
227 / 272= 0.83455882352941176470588235294118
0.83455882352941176470588235294118 x 27= 23 students
From these calculations I can see that if I were to draw a graph, then I would have too many points for the non blonde-haired, blue-eyed students and very little for the blonde-haired, blue-eyed students. I have now decided to increase the sample for the blonde-haired, blue-eyed students to 50%. The reason as to why I have chosen this particular percentage is that I thought it would be the closest number to the non blonde-haired, blue-eyed students. The reason as to why I had thought this was that if 10% = 3, then the closest number to 23 would be multiplying it by 0.50 (50%). Therefore it would be 4 x 5= 20.
Year 8 (blonde-haired, blue-eyed students):
45 / 272= 0.16544117647058823529411764705882
0.16544117647058823529411764705882 x 136= 22 students
Now as you can see, the number of students that I will display for the blonde-haired, blue-eyed students is a much larger number and I will now be able to draw a meaningful conclusion from any graphs that I may show.
Year 9 (blonde-haired, blue-eyed students):
43 / 261= 0.16475095785440613026819923371648
0.16475095785440613026819923371648 x 26= 4 students
Year 9 (non blonde-haired, blue-eyed students):
217 / 261= 0.83141762452107279693486590038314
0.83141762452107279693486590038314 x 26= 22 students
From these calculations I can see again that if I were to draw a graph, then I would have too many points for the non blonde-haired, blue-eyed students and very little for the blonde-haired, blue-eyed students. That is why I have decided to increase the sample for the blonde-haired, blue-eyed students to 50%. The reason as to why I have chosen this particular percentage is that I thought it would be the closest number to the non blonde-haired, blue-eyed students. The reason as to why I had thought this was that if 10% = 3, then the closest number to 23 would be multiplying it by 0.50 (50%). Therefore it would be 4 x 5= 20.
Year 9 (blonde-haired, blue-eyed students):
43 / 261= 0.16475095785440613026819923371648
0.16475095785440613026819923371648 x 130.5= 22 students
Now as you can see, the number of blonde-haired, blue-eyed students has increased to a far greater number. This will help me in drawing a meaningful conclusion from any graphs that may be drawn.
The revised amounts are as follows:
Year 7 (blonde-haired, blue-eyed students):
35 / 283= 0.12367491166077738515901060070671
0.12367491166077738515901060070671 x 212.25= 26 students
Year 7 (non blonde-haired, blue-eyed students):
248 / 283= 0.87632508833922261484098939929329
0.87632508833922261484098939929329 x 28= 25 students
Year 8 (blonde-haired, blue-eyed students):
45 / 272= 0.16544117647058823529411764705882
0.16544117647058823529411764705882 x 136= 22 students
Year 8 (non blonde-haired, blue-eyed students):
227 / 272= 0.83455882352941176470588235294118
0.83455882352941176470588235294118 x 27= 23 students
Year 9 (blonde-haired, blue-eyed students):
43 / 261= 0.16475095785440613026819923371648
0.16475095785440613026819923371648 x 130.5= 22 students
Year 9 (non blonde-haired, blue-eyed students):
217 / 261= 0.83141762452107279693486590038314
0.83141762452107279693486590038314 x 26= 22 students
Random Sampling
Year 7 (non blonde-haired, blue-eyed students):
Ran# x 248=
117
215
232
132
64
238
19
180
184
13
57
65
2
61
159
189
140
4
97
8
197
66
171
225
210
116
Names:
Jervis, Peter
Spencer, Joshua
Victor, Armin
Kent, Emma
Cullen, Sarah
White, Catherine
Barnes, Chloe
O’Farrell, Mihkayla
O’Solomon, Mikeal
Andrews, John
Cook, Melissa
Cullian, Sabor
Afsal, Oliver
Croft, James
Maynard, Fred
Patel, Sean
Lillie, Ben
Ahmed, DJ
Heath, Adam
Anderson, Zahrah
Rider, Andrew
Cunningham, Lindsay
Molloy, Andy
Thompson, Aaton
Smith, Amrit
Jebron, Aysham
Random Sampling
Year 7 (blonde-haired, blue-eyed students):
Ran# x 35=
27
33
26
02
22
19
10
23
20
16
28
07
25
11
30
14
12
09
06
08
24
01
29
18
17
05
Names:
Spencer, Michael
White, Christina
Solecki, Charlotte
Anderson, Lisa
Platt, Sarah
Masters, William
Dodman, Emma
Richards, Abbie
Mills, Robert
Hardings, Tanya
Spencer, Angela
Collins, Jonathon
Smith, Mary
Dugan, Maggie
Toad, Adnal
Glover, Danny
Earnshaw, Kayleigh
Davies, Louise
Cohen, Neil
Croft, Trisha
Shaw, Paul
Anderson, Kylie
Taylor, Charlotte
Lodge, Aaron
Hartnett, Sarah-Jane
Campble, Stephen
Random Sampling
Year 8 (non blonde-haired, blue-eyed students):
Ran# x 227=
216
203
131
61
45
121
56
157
214
153
134
128
218
30
01
29
209
41
40
10
225
189
32
Names:
Walker, John
Steavenson, Ben
Leigh, Adele
Dickinson, Aqued
Channerby, Jane
Kelly, Vicky
Dawson, Elliot
Mohammed, Ashtina
Vector, Armin
Milk, John
Lilten, Abegail
Large, Stephen
Watson, Bethany
Bowling, Mark
Abbott, Zahrah
Bowler, Gerald
Toms, John
Casy, Matthew
Cassel, Diane
Angus, Laura
Wood, Andrew
Shady, Philip
Burke, James
Random Sampling
Year 8 (blonde-haired, blue-eyed students):
Ran# x 45=
29
04
40
25
30
39
43
44
28
31
21
24
03
27
26
32
01
45
10
06
05
02
Names:
Hiccup, Jana-Sarah
Banken, Lilly
Shane, Paul
Hall, Gary
Holliwell, Claire
Rose, Linda
Walker, David
Whitworth, Justine
Hendra, Tina
Houseson, Lisa
Freeman, Ian
Giles, Nichole
Ashton, Luke
Hanten, Victoria
Hanley, Gemma
Kudray, Rebecca
Alfred, Anthony
Willson, Anthony
Boye, Jay
Berry, Alice
Bath, Arthur
Anderson, Kylie
Random Sampling
Year 9 (non blonde-haired, blue-eyed students):
Ran# x 218=
56
194
104
3
4
91
140
163
26
168
155
83
165
99
98
88
69
70
87
57
202
62
Names:
Cranshaw, James
Suggat, Bob
Jasper, Elizabeth
Agha, Hosiab
Agha, Hosaib
Haugh, Jason
McAther, Dougie
Read, Louise
Bigglesworth, Wayne
Rogerson, Claire
Padd, Lilly
Guzman, Victoria
Rites, Auther
Humza, Asim
Hulme, Louise
Hardy, Matt
Edwards, John
Elliot, William
Hardman, Rachael
Crawford, Jamie
Todd, Charlotte
Derd, Amy
Random Sampling
Year 9 (blonde-haired, blue-eyed students):
Ran# x 43=
42
19
03
36
22
26
20
05
08
14
31
21
16
32
11
29
15
24
01
02
37
18
Names
Waugh, Melaine
Henman, Tony
Brown, Caroline
Patricison, Gemma
Hughes, Charelle
Johnson, Emma
Higgins, Jade
Burn, Suzanne
Byrne, Nicola
Greenhalsh, Stacy
Malady, Anthony
Huggard, Malcolm
Haque, Karen
Marsh, Bubble
Crisley, Pheonia
Kalidas, Jessica
Grey, Elizabeth
James, Jordan
Barlow, Sandra
Brooder, Andrew
Right, Tina
Hardy, Ingrid
I will now be comparing the IQ of the blonde haired, blue eyed students in each year. I will also use this to compare the IQ of blonde-haired and blue-eyed students in each year with their non blonde-haired and blue-eyed counterparts by showing how spread out the standard deviation is across the mean value.
Standard Deviation
I will be measuring the dispersion of the IQ from the mean.
To do this I will be using the formula:
∑X2
n
Year 7 (non blonde-haired, blue-eyed students)
Mean: 99.9 (1dp)
∑X2 270743 10027.5
n 27
10027.5 – m2
➔ 10027.5 – 9980.01
S2= 47.49
➔ √47.49= 6.89
➔ 6.9 (1dp)
Year 7 (blonde-haired, blue-eyed students)
Mean: 102.3 (1dp)
∑X2 273301 10511.6
n 26
10511.6 – m2
➔10511.6 – 10465.3
S2= 46.3
➔ √46.3= 6.80
➔ 6.8 (1dp)
Year 8 (non blonde-haired, blue-eyed students)
Mean: 95.6
∑X2 241019 10042.5
n 24
10042.5 – m2
➔ 10042.5 – 9139.4
S2= 903.1
➔ √903.1= 30.05
➔ 30.1 (1dp)
Year 8 (blonde-haired, blue-eyed students)
Mean: 99.7
∑X2 230887 10038.6
n 23
10038.6 – m2
➔ 10038.6 – 9940.1
S2= 98.5
➔ √98.5= 9.92
➔ 9.9 (1dp)
Year 9 (non blonde-haired, blue-eyed students)
Mean: 103.4
∑X2 238572 10844.2
n 22
10844.2 – m2
➔ 10844.2 – 10691.6
S2= 152.4
➔ √152.4= 12.34
➔ 12.3 (1dp)
Year 9 (blonde-haired, blue-eyed students)
Mean: 100.9
∑X2 225228 10237.6
n 22
10237.6 – m2
➔ 10237.6 – 10180.8
S2= 56.8 ➔ √56.8= 7.53 ➔ 7.5 (1dp)
It is evident from the standard deviation that I carried out that in Year 7; the blonde-haired, blue-eyed students are very similar in their intelligence with the students that have a different phenotype. Both groups have a very low dispersion across the mean, which means that hey are all of very similar capabilities and they are all generally clever.
From the standard deviation of Year 8, the blonde-haired, blue-eyed students have a significantly lower deviation across the mean than the students with a different phenotype. The non blonde-haired, blue-eyed students have a dispersion of 30.1 across the mean. This shows that the ability of these students is very widespread. However, as whole, the group is not very intelligent because it is not close to the mean IQ. The blonde-haired, blue-eyed students have however, a much smaller deviation across the mean. This shows that the abilities of the students are very similar to each other. This also means that as a group, the students have a higher intelligence quotient than their counterparts with a different phenotype.
From the standard deviation of Year 9, it is clear to see that the blonde-haired, blue-eyed students are generally more intelligent than their other classmates. This is because the deviation of their IQ is very confined across the mean, compared to the non blonde-haired, blue-eyed students. The non blonde-haired, blue-eyed students have a wider range of IQ across the mean. This means that there is a wiser range of abilities in that group than in the blonde-haired, blue-eyed group. This also means that as a group, the non blonde-haired, blue-eyed students are a less intelligent group than the blond-haired, blue-eyed students.
Year 7 (non blonde-haired, blue-eyed students)
Range: 36
Year 7 (blonde-haired, blue-eyed students)
Range: 30
From the two graphs shown above, it is possible to see that they reflect the values presented by the standard deviation. The graph of the non blonde-haired, blue-eyed students in Year 7 not only has a higher range; it also has a shallower line of best fit.
This means that the students in that sample have a wider range of abilities than the blonde-haired, blue-eyed students. But this also means that the collective intellect of the sample is less than the blonde-haired, blue-eyed sample. The graph shows that the blonde-haired, blue-eyed sample had lower range, and also a steeper line of best fit. This shows that the sample as a group doesn’t have a wide range of abilities. However this means, as is shown by the line of best fit, that the group are intelligent than the non blonde-haired, blue-eyed students.
Year 8 (non blonde-haired, blue-eyed students)
Range: 43
Year 8 (blonde-haired, blue-eyed students)
Range: 42
The graph for the Year 8 (non blonde-haired, blue-eyed sample) shows that the group has a wider range of abilities, ranging form an IQ of 74 to an IQ of 117. This however, also means that the collective intellect of the group is not very high.
The graph for the Year (blonde-haired, blue-eyed sample) does not have such a high range, from an IQ of 71 to an IQ of 113. This shows that the intellect of the students in that sample is very similar. This also means that the collective intelligence is quite high. This is further emphasised by the steepness of the line of best fit.
One observation that can be made about the two graphs is that there is generally a strong positive correlation. However, there are some results that are very widespread from the line of best fit. This shows how widespread the data values as well as the abilities of the students are.
Year 9 (non blonde-haired, blue-eyed sample)
Range: 61
Year 9 (blonde-haired, blue-eyed sample)
Range: 32
From the two graphs above, it is possible to see that the intellect of the two samples is very different. There is a large difference in the two ranges. The non blonde-haired, blue-eyed sample has a range of 61, whereas the range of the blonde-haired, blue-eyed sample is 32. The line of best fit for both of the two groups are very near horizontal. This shows that the collective intellect of the two samples is very similar. However, looking at their respective ranges, it is possible to see that one of the two groups is cleverer than the other. The blonde-haired, blue-eyed sample has a lower range of 32, compared to the non blonde-haired, blue-eyed sample that has a range of 61. This shows that one sample (non blonde-haired, blue-eyed) has a wider range of abilities. The blonde-haired, blue-eyed sample, however, has a lesser range of abilities. This could also mean that the blonde-haired, blue-eyed students are generally more intelligent than their counterparts with a different phenotype.
I can now correctly say, that from the various calculation that I carried out and the graphs that I showed; blonde-haired, blue-eyed students are generally more intelligent that students with different phenotype. Although non blonde-haired, blue-eyed students have a wider range of abilities, this does not meant that as a group, they are very intelligent. The blonde-haired, blue-eyed students are generally more intelligent because they have a smaller range of abilities, but their intelligence quotient is very similar to each other. Their IQ is very confined, when it comes to the spread across the mean.
To check if my conclusion really stands firm, I will further check with the aid of graphs (whisker box plots etc.) if they back up my conclusion.
In descriptive statistics, a box plot (also known as a box-and-whisker diagram or plot or candlestick chart) is a convenient way of graphically depicting the five-number summary, which consists of the smallest observation, lower quartile (Q1), median, upper quartile (Q3), and largest observation; in addition, the box plot indicates which observations, if any, are considered unusual, or outliers. The box plot was invented in 1977 by American statistician John Tukey.
Box plots are able to visually show different types of populations, without any assumptions of the statistical distribution. The spacing between the different parts of the box helps indicate variance, skew and identify outliers. Box plots can be drawn either horizontally or vertically.
Year 7 (both samples)
The two box plots above back up my conclusions that I derived from the scatter graphs that I used to show the IQ of the two different samples for Year 7.
Year 8 (both samples)
Again, these whisker box plots back up the conclusions that I derived from the scatter graphs that I used to show the IQ of the two different samples of Year 8.
Year 9 (both samples)
Just as before, the whisker box plots above, back up the conclusions that I derived from the scatter graphs that I used to show the IQ of the two different samples of Year 9.
The box plots have all backed my conclusions that I gathered from the scatter graphs that were drawn using the IQ of both the blonde-haired, blue-eyed students and the non blonde-haired, blue-eyed students in all the year groups.
When I first started, I was investigating the truth behind the theory that “Blonde haired, blue eyed people are better than others” brought out by Adolf Hitler. I will be trying to see if blonde haired, blue eyed people are generally better than people with other types of hair and eye colour. I wanted to see which statement was truer, Adolf Hitler’s or the general stereotypical theory that all blonde-haired, blue-eyed people are “all play, no work” in other words, air-heads.
From the various calculations that I carried out, and the conclusions that I have gathered from the different types of graphs that were drawn, I can say that generally blonde-haired, blue-eyed students are more intelligent than their student counterparts with different phenotypes. Therefore, it seems that Adolf Hitler was not talking just racist nonsense; his theory does seem to have some truth behind it.
I believe I have gained substantial evidence, and have shown with it, that blonde-haired, blue-eyed students in each year have very similar IQ. Their abilities do not vary a lot, and all of them are generally similar in their capabilities.
http://en.wikipedia.org/wiki/Box_plot
