Compare the heights and weights of pupils from Mayfield high school.
Maths GCSE Coursework
(Mayfield High)
My task is to compare the data of Mayfield high school children. My hypothesis in this task are shown below, I will use my data to show if my line of enquire is right or wrong and if so why.
* Older pupils are tall/heavier.
* The older the pupil the heavier they are.
In this data I will compare the heights and weights of pupils from year 7 to year 11 and males and females, I am going to use data from different years because I would like to see if age makes a difference, also I am comparing both sexes to see if that differs.
As it stand there is more boys than girls in the school and some of the years group are bigger than others, shown below:
Year
Boys
Girls
Total
7
40
31
271
8
45
21
266
9
18
43
261
0
08
94
202
1
84
86
70
595
572
170
I have taken into account that some years are bigger than others, and there is more boys in the school so I have decided to take a certain amount of boys and girls from each year, my calculation are shown below:
Yr 7 b = 140/595x30= 7
Yr 7 g = 131/575x30= 7
Yr 8 b = 145/595x30= 7
Yr 8 g = 121/575x30= 6
Yr 9 b = 118/595x30= 6
Yr 9 g = 143/575x30= 7
Yr 10 b = 108/595x30= 5
Yr 10 g = 94/575x30= 5
Yr 11 b = 84/595x30= 4
Yr 11 g = 86/575x30= 4
From this I then when on and created random number from the equation on a scientific calculator:
[Shift] [.] [x] [30].
After that I went and picked the pupil with the same number and I did this for the amount of pupils I needed for each section.
Mayfield High Frequency Table For Height
Year 7
Height (cm)
Tally
Frequency
Midpoint
Frequency x
Midpoint
Cumulative Frequency
20?h<130
I
25
x125=125
30?h<140
II
2
35
2x135=270
3
40?h<150
III
3
45
3x145=435
5
50?h<160
IIIII
5
55
5x155=775
8
60?h<170
III
3
65
3x165=495
3
70?h<180
0
75
0x175=0
6
80?h<190
0
85
0x185=0
6
Totals
4
2100
6
Mean 2100/14=150cm
Median 8
Mode 150?h<160cm
Range 14
Upper Quartile 12
Lower Quartile 4
Interquartile Range 8
Year 8
Height (cm)
Tally
Frequency
Midpoint
Frequency x
Midpoint
Cumulative Frequency
20?h<130
0
25
0x125=0
0
30?h<140
0
35
0x135=0
0
40?h<150
II
2
45
2x145=290
0
50?h<160
IIIII
4
55
4x155=620
2
60?h<170
IIIII
4
65
4x165=660
6
70?h<180
II
2
75
2x175=350
0
80?h<190
I
85
x185=185
2
Totals
3
2105
3
Mean 2105/13= 161.9cm to 1d.p.
Median 6
Mode 150?h<160cm
Range 13
Upper Quartile 9
Lower Quartile 3
Interquartile Range 6
Year 9
Height (cm)
Tally
Frequency
Midpoint
Frequency x
Midpoint
Cumulative Frequency
20?h<130
0
25
0x125=0
0
30?h<140
0
35
0x135=0
0
40?h<150
I
45
x145=145
0
50?h<160
III
3
55
3x155=465
60?h<170
IIII
4
65
4x165=660
4
70?h<180
IIIII
5
75
5x175=875
8
80?h<190
0
85
0x185=0
3
Totals
3
2145
3
Mean 2145/13=165cm
Median 6.5
Mode 170?h<180cm
Range 13
Upper Quartile 9.75
Lower Quartile 3.25
Interquartile Range 6.5
Year 10
Height (cm)
Tally
Frequency
Midpoint
Frequency x
Midpoint
Cumulative Frequency
20?h<130
0
25
0x125=0
0
30?h<140
0
35
0x135=0
0
40?h<150
II
2
45
2x145=290
0
50?h<160
II
2
55
2x155=310
2
60?h<170
IIIII
5
65
...
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Median 6.5
Mode 170?h<180cm
Range 13
Upper Quartile 9.75
Lower Quartile 3.25
Interquartile Range 6.5
Year 10
Height (cm)
Tally
Frequency
Midpoint
Frequency x
Midpoint
Cumulative Frequency
20?h<130
0
25
0x125=0
0
30?h<140
0
35
0x135=0
0
40?h<150
II
2
45
2x145=290
0
50?h<160
II
2
55
2x155=310
2
60?h<170
IIIII
5
65
5x165=825
4
70?h<180
II
2
75
2x175=350
9
80?h<190
0
85
0x185=0
1
Totals
1
775
1
Mean 1775/11=161.4cm to 1d.p.
Median 5.5
Mode 160?h<170cm
Range 11
Upper Quartile 8.25
Lower Quartile 2.75
Interquartile Range 5.5
Year 11
Height (cm)
Tally
Frequency
Midpoint
Frequency x
Midpoint
Cumulative Frequency
20?h<130
0
25
0x125=0
0
30?h<140
0
35
0x135=0
0
40?h<150
0
45
0x145=0
0
50?h<160
II
2
55
2x155=310
0
60?h<170
IIII
4
65
4x165=660
2
70?h<180
I
75
x175=175
6
80?h<190
II
2
85
2x185=370
7
Totals
9
515
9
Mean 1515/9=168.3cm to 1 d.p.
Median 3.5
Mode 160?h<170cm
Range 9
Upper Quartile 5.25
Lower Quartile 1.75
Interquartile Range 3.5
Mayfield High Frequency Polygon (Height)
Year 7
Year 8
Year 9
Year10
Year 11
Mayfield High Frequency Table for Weight
Weight (kg)
Tally
Frequency
Midpoint
Frequency x Midpoint
Cumulative Frequency
20?w<30
0
25
0x25=0
0
30?w<40
III
3
35
3x35=105
0
40?w<50
IIIIIIIIII
0
45
0x45=450
3
50?w<60
I
55
x55=55
3
60?w<70
0
65
0x65=0
4
70?w<80
0
75
0x75=0
4
Totals
4
610
4
Mean 610/14=43.57 to 2 d.p
Median 7.5
Mode 40
Range 14
Upper Quartile 9.25
Lower Quartile 3.75
Interquartile Range 7.5
Year 7
Year 8
Weight (kg)
Tally
Frequency
Midpoint
Frequency x Midpoint
Cumulative Frequency
20?w<30
I
25
x25=25
0
30?w<40
I
35
x35=35
40?w<50
III
3
45
3x45=135
2
50?w<60
IIIII
5
55
5x55=275
5
60?w<70
I
65
x65=65
0
70?w<80
II
2
75
2x75=150
1
Totals
3
685
2
Mean 685/13=52.69 to 2 d.p
Median 5.5
Mode 50
Range 13
Upper Quartile 8.25
Lower Quartile 2.75
Interquartile Range 5.5
Year 9
Weight (kg)
Tally
Frequency
Midpoint
Frequency x Midpoint
Cumulative Frequency
20?w<30
0
25
0x25=0
0
30?w<40
I
35
x35=35
0
40?w<50
IIIII
5
45
5x45=225
50?w<60
III
3
55
3x55=165
6
60?w<70
IIII
4
65
4x65=260
9
70?w<80
0
75
0x75=0
3
Totals
3
685
3
Mean 685/13=52.69 to 2 d.p
Median 6.5
Mode 40?w<50kg
Range 13
Upper Quartile 9.75
Lower Quartile 3.25
Interquartile Range 6.5
Year 10
Weight (kg)
Tally
Frequency
Midpoint
Frequency x Midpoint
Cumulative Frequency
20?w<30
0
25
0x25=0
0
30?w<40
0
35
0x35=0
0
40?w<50
II
2
45
2x45=90
0
50?w<60
IIIIII
6
55
6x55=330
2
60?w<70
III
3
65
3x65=195
8
70?w<80
0
75
0x75=0
1
Totals
1
615
1
Mean 615/11=55.91 to 2 d.p
Median 5.5
Mode 50?w<60kg
Range 11
Upper Quartile 8.25
Lower Quartile 2.75
Interquartile Range 5.5
Year 11
Weight (kg)
Tally
Frequency
Midpoint
Frequency x Midpoint
Cumulative Frequency
20?w<30
0
25
0x25=0
0
30?w<40
I
35
x35=35
0
40?w<50
II
2
45
2x45=90
50?w<60
III
3
55
3x55=165
3
60?w<70
I
65
x65=65
6
70?w<80
II
2
75
2x75=150
7
Totals
9
505
9
Mean 505/9=56.11 to 2 d.p
Median 3.5
Mode 50?w<60kg
Range 9
Upper Quartile 5.25
Lower Quartile 1.75
Interquartile Range 3.5
Mayfield High Frequency Polygon (Weight)
First hypothesis
Older pupils are taller
My first line of enquiry was to find out if people as they got older in a school they also became taller. I thought this maybe true because of people growing. I took my data in centimetres so that the data was more accurate to reduce any errors in the data.
With the median I have noticed that as the years get greater the median gets lower. For example in year 7 the median is 8 but where as in year 11 the median is 3.5. But I have found that there is an error in the data because in year 9 the median is 6.5 where as in year 8 it is only 6. This could be because there are different people and so different people grow more or less.
I have found that in year 11, the mean is higher than in any other year group, and year 7 had the lowest mean.
Also I can see that as the year groups increase the range decreases this could be because as you get older you start to grow less and so the range between the tallest and the smallest starts to narrow.
I can see by my cumulative frequency curve that year 7 has the highest cumulative frequency in the tallest height group.
In year 7 the group with the highest frequency was the 150?h<160cm. In year 8 the group with the highest frequency was 150?h<160cm and 160?h<170cm. Where as in year 9 the biggest group was 170?h<180cm. The biggest year 10 group was 160?h<170cm, and in year 11 the biggest group was 160?h<170cm.
So I have come to the conclusion that from the data I have look at, people as they get older do grow but the gap between the smallest and the tallest does narrow. Where as the year with the biggest height group was year 9 with 170?h<180cm. But I can see with my cumulative frequency curve that year 7 has the highest total cumulative frequency where as year 11 has the lowest cumulative frequency. So from this I can say that not in every case older people are taller.
First hypothesis
Older pupils are taller
I am going to collect some data. The data that I will gather will be on the heights of children from the years 7, 8, 9, 10, and 11. With this data I am going to compare it and come to the conclusion whether my theory is correct or incorrect. The theory that I have is 'older pupils are taller'.
I am going to pick some student by using calculation so that they are random, and so this doesn't interfere with the data causing errors. I am going to make sure that I get boys and girls on the data tables so that I am not just comparing the age and certain sex for the height. So I will make sure that the years have mixed sexes so that I don't have biased data.
With my data I will sort it into groups and then compare the different groups with the age. The groups that I will sort the data into are shown below:
* 120?h<130cm
* 130?h<140cm
* 140?h<150cm
* 150?h<160cm
* 160?h<170cm
* 170?h<180cm
* 180?h<190cm
Also with the data I am going to find the lower quartile, upper quartile, Interquartile range, median, mean, and mode. So then I can compare the results from different years to come to my final conclusion.
How I found the Lower Quartile, Upper Quartile,
Interquartile Range, Range, Median, Mode, and Mean
Using the data I found from Mayfield High. I put the data I gathered into a table with a cumulative frequency column on the table, after that I started to plot a cumulative frequency graph, with a cumulative frequency curve on it. With this I can now find out what the Lower Quartile, Upper Quartile, Median and Interquartile Range are.
To find the Lower Quartile you must first find the midpoint of the cumulative frequency. This is called the median. From this you can halve the median to get the Lower Quartile this is the number half way between the median and 0. For the Upper Quartile you must again halve the median and find the half way point between the median and the total cumulative frequency. Finally the Interquartile Range is the difference between the Lower Quartile and the Upper Quartile.
Mean is the average of the data, this is found by:
Mean = Overall Total (Final Row)
Frequency Total (2nd Row)
The mode is the group with the most entries (the highest frequency). So to find this all you have to do is look at the table and find out which group has the highest frequency.
I am going to find the Upper Quartile, Lower Quartile, Interquartile Range, Mean, Mode, and Median so that I can compare these to other years of children. Then I can come to the conclusion whether my hypotheses are correct or incorrect and why.
Second hypothesis
Older pupils are heavier
For this hypothesis I will gather some weight data from 'Mayfield High School'. With this data I will use different years so that I can compare them and find out whether 'older pupils are heavier'.
With this data I will sort it into different weight group this is so at the end I can analysis whether the older a person get the heavier they become. The groups that I will sort the data in are shown below:
* 20?w<30kg
* 30?w<40kg
* 40?w<50kg
* 50?w<60kg
* 60?w<70kg
* 70?w<80kg
Also with the data I am going to find the lower quartile, upper quartile, Interquartile range, median, mean, and mode. So then I can compare the results from different years to come to my final conclusion.
How I found the Lower Quartile, Upper Quartile,
Interquartile Range, Range, Median, Mode, and Mean
Using the data I found from Mayfield High. I put the data I gathered into a table with a cumulative frequency column on the table, after that I started to plot a cumulative frequency graph, with a cumulative frequency curve on it. With this I can now find out what the Lower Quartile, Upper Quartile, Median and Interquartile Range are.
To find the Lower Quartile you must first find the midpoint of the cumulative frequency. This is called the median. From this you can halve the median to get the Lower Quartile this is the number half way between the median and 0. For the Upper Quartile you must again halve the median and find the half way point between the median and the total cumulative frequency. Finally the Interquartile Range is the difference between the Lower Quartile and the Upper Quartile.
Mean is the average of the data, this is found by:
Mean = Overall Total (Final Row)
Frequency Total (2nd Row)
The mode is the group with the most entries (the highest frequency). So to find this all you have to do is look at the table and find out which group has the highest frequency.
I am going to find the Upper Quartile, Lower Quartile, Interquartile Range, Mean, Mode, and Median so that I can compare these to other years of children. Then I can come to the conclusion whether my hypotheses are correct or incorrect and why.
Second Hypothesis
Older pupils are heavier
My second line of enquiry was to find out whether as a pupil got older they also became heavier. For this I have gathered data and sorted into groups and processed the data into tables and graphs, from this I can now look at the data and come to the conclusion on whether my theory was correct or not and why.
From my data I can see that year 11 had the lowest median from all the year groups, and I can also see that year 7 have the highest median. This could because of growth which causes the weight to increase, but also the diet of the child may increase or decrease the weight of the child.
Year 8 and Year 10 had the highest frequency in the biggest weight group. But year 8 has the highest frequency in the lowest weight group as well, so this shows that there is a big gap between the weights of the children in year 8.
I can also see from my data tables that year 7 has the biggest range out of the whole year groups. Year 7 also had the highest lower quartile. The biggest upper quartile was found in year 9, and the average mode of the entire year groups was 50?w<60kg.
So I have now come to the conclusion that age doesn't play a massive factor in the weight of a child if could also be because of the diet that they eat. But I have found from the children that I use for my data that the weight did increase as they got older and this is mainly due to growing, so this changes the weight of the child.
Thomas Ordidge Maths
Miss Vickers 10JG GCSE Coursework
