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• Level: GCSE
• Subject: Maths
• Word count: 2387

# 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 Gradex 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 intervalx 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

 IQx Middle point of the class intervalx 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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