Data handling coursework: Mayfield High School
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Introduction
Benjy Levey Data handling coursework
Data handling coursework: Mayfield High School
I have been given the data for 1183 students at a fictional school. The data is however not fictional. Different data is recorded for each student and ranges from their names, ages, height, weight, together with IQ, school results etc… I have chosen to investigate the relationship between height and weight. I think that this will be a more varied investigation unlike the relationship between eye colour and hair colour, as it is pretty random which colour eyes and hair you have and does not have anything in common.
All the information given us is too much for us to use, and therefore I have selected only a small amount of data for each student, which will be relevant to the height and weight of each student.
As 1183 students are far too many to many to analyse correctly, I have taken ten people from each year group, five random boys and five random girls. First I sorted my data into years and gender and once they were separate I used the random number button on my calculator (ran# button)
Middle
Tally
Frequency
120 ≤ h < 130

1
130 ≤ h < 140
0
140 ≤ h < 150

4
150 ≤ h < 160
 
9
160 ≤ h < 170
 
8
170 ≤ h < 180

2
180 ≤ h < 190

1
Weight, w (kg)  Tally  Frequency 
20 ≤ w < 30    1 
30 ≤ w < 40    4 
40 ≤ w < 50    15 
50 ≤ w < 60    4 
60 ≤ w < 70    1 
70 ≤ w < 80  0 
I will then show these tally charts above onto four separate bar graphs each relating to boys/girls height and weight.
To make these graphs clearer to see, I will present the data in the form of two frequency polygon; one for girls and boys height, and one for girls and boys weight.
I can see from the frequency polygon that there are more girls with heights between 150 and 170cm than boys, but there are only a few more boys taller 170cm. This would suggest that possibly my hypothesis was not correct as there isn’t that much of a difference between boys and the girls.
This shows that the Boys’ data is more spread out than the girls. It also shows that there are fewer boys with weights between 20 and 60kg than girls. There are however more boys with weights higher than 60kg.
Averages for the data.
By looking at my frequency tables I will be able to determine what the mean, mode, median and range of all my data will be. From discovering these, I will be able to determine whether my hypothesises were correct. In order to find all these factors I will have to produce another frequency table.
Boys  
Height, h (cm)  frequency  midpoint  Fx = midpoint x frequency 
130 ≤ h < 140  1  135  135 
140 ≤ h < 150  2  145  290 
150 ≤ h < 160  3  155  465 
160 ≤ h < 170  6  165  990 
170 ≤ h < 180  10  175  1750 
180 ≤ h < 190  2  185  370 
190 ≤ h < 100  1  195  195 
∑f = 25  ∑fx = 4195 
Conclusion
Girls  
Height, h (cm)  frequency  midpoint  fx = midpoint x frequency 
120 ≤ h < 130  1  125  125 
130 ≤ h < 140  0  135  0 
140 ≤ h < 150  4  145  580 
150 ≤ h < 160  9  155  1395 
160 ≤ h < 170  8  165  1320 
170 ≤ h < 180  2  175  350 
180 ≤ h < 190  1  185  185 
=  ∑f = 25  ∑fx = 3955 
The range in boys weights: 69 – 29 = 40kg
The mode for this data is: 140 ≤ h < 150.
The mean for this date is : x = ∑fx = 3955 = 158.2
∑f 25
The median for this data is: 150 ≤ h < 160
The range in girls’ heights is : 1.83 – 1.42 = 0.41m
girls  
Weight, w (kg)  frequency  midpoint  fx = midpoint x frequency 
20 ≤ w < 30  1  25  25 
30 ≤ w < 40  4  35  140 
40 ≤ w < 50  15  45  675 
50 ≤ w < 60  4  55  220 
60 ≤ w < 70  1  65  65 
70 ≤ w < 80  0  75  0 
=  25  1125 
The mode of this data is: 40 ≤ h < 50.
The mean for this data is: x = ∑fx = 1125 = 45
∑f 25
The median for this data lies within the data is: 40 ≤ h < 50
The mean for this data is: x = ∑fx = 1315 = 52.6
∑f 25
The median for this data lies within the data is: 40 ≤ h < 50.
The range for girls’ weight is: 60 – 29 = 31
mode  mean  median  range  
boys heights  70 ≤ h < 180  167.8  170 ≤ h < 180  0.57 
boys weights  50 ≤ h < 60.  52.6  50 ≤ h < 60  40 
girls heights  140 ≤ h < 150  158.2  150 ≤ h < 160  0.41 
girls weights  40 ≤ h < 50  45  40 ≤ h < 50  31 
I have discovered that, after working out the mean of both the boys’ and girls heights and weights, that in fact the both the boys height and weights are higher than the girls’. This proves that my hypothesis is correct.
Page
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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