Comparing IQ at school.
Extracts from this document...
Introduction
Statistics
Hypothesis: I think, that the girls science results are better than the boys science results compared with their IQ, because girls are more intelligent in science than boys in year 11.
BOYS
Number  Science  IQ  
1  1019  4  113 
2  1020  5  105 
3  1026  3  89 
4  1033  4  106 
5  1036  3  76 
6  1027  5  119 
7  1068  5  106 
8  1065  4  101 
9  1077  6  107 
10  1075  5  103 
11  1066  4  104 
12  1122  4  104 
13  1138  2  78 
14  1135  5  127 
15  1128  5  122 
16  1043  5  110 
17  1057  5  110 
18  1085  5  124 
19  1095  3  90 
20  1086  3  97 
21  1081  3  98 
22  1076  3  102 
23  1090  4  98 
24  1130  3  89 
25  1141  5  14 
26  1124  5  110 
27  1146  3  86 
28  1140  5  107 
29  1156  4  100 
30  1157  3  101 
GIRLS
Number  Science  IQ  
1  1016  4  104 
2  1023  4  102 
3  1018  4  28 
4  1017  4  26 
5  1067  4  95 
6  1070  4  112 
7  1071  4  104 
8  1087  3  92 
9  1097  3  90 
10  1031  4  98 
11  1026  4  106 
12  1136  5  106 
13  1132  4  102 
14  1137  5  107 
15  1125  4  101 
16  1082  3  187 
17  1081  5  108 
18  1037  3  91 
19  1030  6  126 
20  1047  4  104 
21  1029  4  100 
22  1046  5  110 
23  1032  5  104 
24  1140  4  100 
25  1114  3  98 
26  1105  4  100 
27  1174  4  101 
28  1180  4  88 
29  1107  4  97 
30  1127  4  104 
I get these information about the students in Mayfield High School from the grid which shows the whole year 11 students. Altogether there are 84 boys and 86 girls which gives a total of 170 students.
I chose the numbers of boys and girls randomly by throwing two dices at the same time. For example at the boys table, the first number which is 1019. I threw the two dices and one dice showed 6 and the other showed 3. I add them up and the answer was 9. On the table of all the year 11 students (boys and girls) the number which starts 9 at the ending was the randomly chosen number. I chose them all in the same way and the girls
too (up to 30 boys and 30 girls) randomly. Then I write down their science results in one column and their IQ in another column.
First I will calculate the find the frequency for the boys and girls of their science results. To have the results detailed and clear. I will draw a whisker box diagram, scatter graphs and other statistical diagrams to support my frequency results in the table below.
Middle

7
28
5

12
60
6

1
6
Σf=30
Σfx=123
Mean ,Using the formula : x = Σfx Σf  4 
Mode  5 
Median  5 
Range  4 
GIRLS
Science Grade x  Tally  Number of Students (Frequency) f  fx 
1  0  0  
2  0  0  
3    5  15 
4    19  76 
5    5  25 
6    1  6 
Σf=30  Σfx=122 
Mean ,Using the formula : x = Σfx Σf  4 
Mode  4 
Median  4 
Range  5 
BOYS
IQ  Middle point of the class interval x  Tally  Number of Students (Frequency) f  fx 
10≤IQ<20  15    1  15 
20≤IQ<30  25  0  0  
30≤IQ<40  35  0  0  
40≤IQ<50  45  0  0  
50≤IQ<60  55  0  0  
60≤IQ<70  65  0  0  
70≤IQ<80  75    2  150 
80≤IQ<90  85    3  255 
90≤IQ<100  95    4  380 
100≤IQ<110  105    13  1365 
110≤IQ<120  115    4  460 
120≤IQ<130  125    3  375 
Σf=30  Σfx=3000 
Mean ,Using the formula : x = Σfx Σf  100 
Model class  100≤IQ<110 
Median  94 
Range  113 
GIRLS
IQ x  Middle point of the class interval x  Tally  Number of Students (Frequency) f  fx 
10≤IQ<20  15  0  0  
20≤IQ<30  25    2  50 
30≤IQ<40  35  0  0  
40≤IQ<50  45  0  0  
50≤IQ<60  55  0  0  
60≤IQ<70  65  0  0  
70≤IQ 
Conclusion
Bar chart and Histogram
I have drawn the bar chart for Science grade attained among boys and girls, because these are discrete data. Histogram is more appropriate in the case of IQ because these are continuous data. From both these diagrams mean, mode and median can be calculated
Frequency polygon
From the frequency polygon I can find that the more number of boys the have value of IQ (115) than girls.
Stem and Leaf Diagram
I have drawn a stem and leaf diagram because IQ data are continuous and are grouped into class interval.
Stem and leaf diagram for IQ
Boys
Stem  Leaf  F 
1  4  1 
7  6 8  2 
8  6 9 9  3 
9  0 7 8 8  4 
10  0 1 1 2 3 4 4 5 6 6 7 7  12 
11  0 0 0 3 9  5 
12  2 4 7  3 
Girls
Stem  Leaf  F 
2  6 8  1 
8  8  2 
9  0 1 2 5 7 8 8  3 
10  0 0 0 1 1 2 2 4 4 4 4 4 6 6 7 8  3 
11  0 2  12 
12  6  5 
18  7  3 
Cumulative frequency table
Science Grade  Cumulative frequency  
Boys  Girls  
1  0  0 
2  1  0 
3  10  5 
4  17  24 
5  29  29 
6  30  30 
IQ  Cumulative frequency  
Boys  Girls  
15  1  0 
25  0  2 
75  3  0 
85  6  4 
95  10  11 
105  23  27 
115  27  29 
125  30  30 
Cumulative frequency graph
Cumulative frequency graph is more appropriate for IQ value rather than science grades.
Because former are continuous data and latter are discrete data.
Science
Boys  Girls  
Range  4  5 
Interquartile range  1.8  0.9 
IQ
Boys  Girls  
Range  113  100 
Interquartile range  22  9 
Interquartile range shows better value of dispersion because it eliminates the extreme values there by distorting the statistical inference. The data of the boys are widely dispersed. Range is not appropriate in this instance.
I have drawn Box and Whisker diagrams for science and IQ.
Summary
The achievement of science grades are better among boys than girls because they have higher value of IQ. The conclusion is based on small samples and further analysis should be made considering larger samples. The samples should also test to show that it represents the true population by sampling techniques.
This student written piece of work is one of many that can be found in our GCSE Height and Weight of Pupils and other Mayfield High School investigations section.
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