- Histogram
These Histograms show that Year 11 males are taller than Year 11 females. The Histogram for Year 11 Males has a Positive Skew, and the Histogram for Year 11 females has a negative skew, which shows that on average there are mainly tall males, and on average the females are small. I can also see that there are very few tall females, and few small males.
2. Mean
Mean Male Height = Sum of Height = 4401.4 = 176.056cm
No. of Pupils 25
Mean Female Height = Sum of Height = 4090.2 = 163.608cm
No. of Pupils 25
From these two figures I can see that an average Year 11 male is 12.448 cm taller than an average Year 11 Female, which as a percentage is 7.1%. This is not far from my prediction of 10% in my Hypothesis. From these calculations I can also see that the combined height of Year 11 Males is 311.2 cm or 7.1% more than the combined height of the Year 11 females.
3. Mode (Modal Group)
Male Mode (Modal Group) = 180 ≤ h < 185 cm
Female Mode (Modal Group) = 160 ≤ h < 165 cm
From these answers I can see that the mode Height for a Year 11 Male is 20cm taller than the mode of Year 11 Female, this is 11.1% ≤ h < 10.8% taller as a percentage, which is almost as I predicted in my Hypothesis.
4. Cumulative Frequency Graph
Here is the table and graph for Male Cumulative Frequency for Height;
Here is my table and graph for Female Cumulative Frequency for Height;
From these graphs for Cumulative frequency I can see that the gradient of the curve for Males is steeper towards the end half of the curve, and the gradient of the curve for Females is steeper at the beginning and then the gradient is very low at the end. This shows that the concentration of smaller pupils is greater for Females, and the concentration for taller pupils is much greater for Male Year 11 pupils. I can also see from the Female Cumulative Frequency graph that there are very few tall female Year 11 pupils, and from the Male Cumulative frequency graph I can see that there are very few small male Year 11 pupils.
5. Median
Male Median Height = 177.5 cm
Female Median Height = 164 cm
From these figures I can see that the Male median Height for a Year 11 pupil is 13.5 cm or 7.6% taller that the median Height for a Year 11 Female, which is not far off my prediction of 10%.
6. Interquartile Range
Male Interquartile Range
= Q3 – Q1 = 183 cm – 170 cm = 13 cm
Female Interquartile Range
= Q3 – Q1 = 167.5 cm – 160.5 cm = 7 cm
Here are my Box and Whisker Diagrams;
From the Interquartile Range and the Box and Whisker diagrams I can see that the middle 50% of the Female height data has a much tighter distribution than the middle 50% of the male height data. From the diagrams I can see that the middle 50% of the male data covers the taller heights, and the middle 50% of the female data covers mainly smaller heights.
7. Standard Deviation
Male Standard Deviation = 8.255
Female Standard Deviation = 6.018
From these calculations I can see that the spread of the data from the mean for Females is much tighter than the spread of the data from the mean for Males.
From these calculations I have found out that an average Year 11 Male is between 7.1% and 11.1% taller than an average Year 11 Female. I will now move on to Weight.
2. Weight (All data)
I will now do all my calculations and graphs for Weight. I will firstly do them for all the data, I will then split it into male and female and repeat the calculations and graphs. Here is my table of grouped data for the weight of Year 11 pupils, including all my data;
1. Histogram
From this Histogram I can see that it has a negative skew, there are three outliers that can be seen on the histogram between 90 and 100. Also, the weights of Year 11 pupils have a tight distribution without the outliers.
2. Mean
Mean = Sum of Weight = 3129.5 = 62.59 Kg
No. of Pupils 50
Compared to my weight of 68 Kg, the mean weight of a Year 11 pupil is 5.41cm smaller than my weight. As a percentage this is 8.0%, which makes my prediction of 10% almost correct.
3. Mode (Modal Group)
Mode (Modal Group) = 55Kg ≤ w < 60Kg
The modal weight for an average Year 11 pupil is 55Kg ≤ w < 60Kg which is 13Kg ≤ w < 8Kg smaller than my weight of 68%. This means my weight is 19.1% ≤ w < 11.8% above average.
4. Cumulative Frequency Graph
Here is my table and graph for the Cumulative frequency for weight;
From this graph I can see that the gradient of the curve is steep up to 80Kg, and then it hardly goes up at all. The flat line in the curve shows that no pupils from my data have a height of between 80Kg and 90Kg.
5. Median
Median = 62 Kg
The median weight of a Year 11 pupil is 6 Kg or 8.8% smaller than my weight of 68 Kg.
6. Interquartile Range
Interquartile Range = Q3 – Q1 = 69.5Kg – 56Kg = 13.5Kg
From the Box and Whisker diagram and the Interquartile range I can see that the middle 50% of the data covers 25% of the total data, which shows that the data in the middle 50% is tightly distributed.
7. Standard Deviation
Standard Deviation = 11.671
From this figure I can see that the data has a high dispersion, and is spread quite far from the mean.
From all the calculations and graphs I have made for weight I have found out that I am between 8.0% and 19.1% heavier than the average Year 11 Pupil. In my hypothesis I predicted I would be 10% heavier, so my prediction was correct.
2. Weight (Male & Female)
I will now split the data into male and female because I want to find out if an average Year 11 Male is 10% heavier than an average Year 11 Female, I will do my calculations and graphs for both and compare the figures and results I get as I go along. Here are the two tables of grouped data for Male and Female Weights;
1. Histogram
From these two Histograms I can see that the data for females seems to show a tighter distribution than the data for males. I can also see from these graphs that the outliers with a high weight all seem to be males. Overall, the gender with mainly small weights seems to be females, and the Year 11 males seem to have heavier weights.
2. Mean
Mean Male Weight = Sum of Weight = 1669.5 = 66.76 Kg
No. of Pupils 25
Mean Female Weight = Sum of Weight = 1460 = 58.4 Kg
No. of Pupils 25
From these results I can see that the mean weight for a Year 11 male is 8.36 Kg more than the mean weight for a Year 11 Female, which is 12.52% heavier on average.
3. Mode (Modal Group)
Male Modal Weight = 55 ≤ w < 60 Kg
Female Modal Weight = 50 ≤ w < 65 Kg
From these figures I can see that the mode for females covers a larger range of weight than the mode weight for males, this is because the frequency for females is the same for three columns in my Histogram.
4. Cumulative Frequency Graph
Here is the table and graph for Male Cumulative Frequency for Weight;
Here is the table and graph for Female Cumulative Frequency for Weight;
From these Cumulative Frequency graphs I can see that the curve for male weight shows a more widely spread set of data around the median, and the curve for female cumulative frequency weight shows a much tighter distribution of data around the median. From the female cumulative frequency graph I can see that no females have a weight of above 75 Kg, but 7 males have a weight above this figure. This shows that more male Year 11 pupils have a heavier weight and female pupils have lighter weights.
5. Median
Male Median Weight = 65 Kg
Female Median Weight = 60 Kg
From these figures I can see the median weight for a female Year 11 pupil is 5 Kg or 7.7% lighter than the median weight for a Year 11 Male Pupil, which is quite close to my prediction of 10%.
6. Interquartile Range
Male Interquartile Range
= Q3 – Q1 = 75 Kg – 58 Kg = 17 Kg
Female Interquartile Range
= Q3 – Q1 = 65 Kg – 53 Kg = 12 Kg
Here are my Box and Whisker Diagrams;
From the Box and Whisker Diagrams and the Interquartile Range I can see that the box for male box and whisker covers slightly heavier weights than the female box from the box and whisker diagram does, this shows that male weights are heavier than female weights. I can also see from these diagrams that the male data is more widely spread than the female data.
7. Standard Deviation
Male Standard Deviation = 13.234
Female Standard Deviation = 8.149
From these figures I can see that the Standard Deviation for males is 38.42% more than the Standard Deviation for Females. This shows that the male weight data is much more widely spread compared to the female data.
From all of my calculations and graphs I have made for the weight of Year 11 males and females I can see that Year 11 Males are on average between 9.52% and 12.52% heavier than Year 11 Females.
3. Arm Span (All Data)
I will now do all my calculations and graphs for Arm Span. I will do them firstly for all the data, to find the average pupils arm span. Then I will split the data into Male and Female and do the calculations and graphs for them, and compare them as I go along. Here is my table of grouped data for the Arm Span of Year 11 pupils, including all my data;
1. Histogram
From this Histogram I can see that it has a slight negative skew, which shows there is a bigger distribution of pupils with a short arm span. I can also see from the graph that there are more pupils with a short arm span than pupils with a long arm span.
2. Mean
Mean Arm Span = Sum of Arm Span = 8452 = 169.04cm
No. of Pupils 50
Compared to my Arm Span of 185cm, the mean Arm Span for a Year 11 Pupil is 15.96cm or 8.63% smaller than my Arm Span.
3. Mode (Modal Group)
Mode (Modal Group) = 165 cm ≤ as < 170 cm
From this I can see that the modal group for Arm Span for a Year 11 Pupil is 20cm ≤ h < 15cm smaller than my Arm Span, or 10.81% ≤ h < 8.11% as a percentage. This proves my prediction of 10% correct.
4. Cumulative Frequency Graph
Here is my table and graph for the Cumulative frequency for Arm Span;
From the Cumulative Frequency Graph above I can see that the gradient of the curve is steep around the median and lower quartile, which shows the data in this area is very close together. But the data after the upper quartile is very spread out because the gradient of the curve is so shallow.
5. Median
Median = 168.5cm
The median Arm Span for a Year 11 Pupil is 168.5 cm which is 16.5cm or 8.92% shorter than my Arm Span, almost what I predicted.
6. Interquartile Range
Interquartile Range = Q3 – Q1 = 176cm – 162.5cm = 13.5cm
From the Interquartile Range and the Box and Whisker Diagram above I can see that the middle 50% of the data covers 13.5cm or 25% of the total data range. This shows that the middle 50% is tightly distributed.
7. Standard Deviation
Standard Deviation = 10.949
From this figure I can see that the data is spread quite far from the mean, showing that the data is quite spread out overall.
From all of the calculations and graphs I have made for the Arm Span of Year 11 Pupils I have found out that my Arm Span is between 15cm and 20cm, or 8.11% and 10.81%.
3. Arm Span (Male & Female)
I will now split the data into male and female because I want to find out if the average Arm Span of Male Year 11 Pupils is 10% longer than the average Arm Span of Female Year 11 Pupils. Here are the two tables of grouped data for Male and Female Arm Span;
1. Histogram
From these Histograms I can see that the male data for Arm Span seems to be far more spread out than the data for females. I can also see that the data for females is distributed around the smaller lengths and the male data is distributed around the longer lengths for Arm Span. Finally I can see that the extreme long lengths for Arm Span are all males, and the extreme short lengths for Arm Span are all females.
2. Mean
Mean Male Arm Span = Sum of Arm Span = 4379cm = 175.16cm
No. of Pupils 25
Mean Female Arm Span = Sum of Arm Span = 4073cm = 162.92cm
No. of Pupils 25
From these results for the Mean Arm Span for male and female data I can see that the mean male Arm Span is 12.24cm or 6.99% longer than the female Arm Span, which is quite close to my prediction of 10%.
3. Mode (Modal Group)
Male Mode (Modal Group) = 175cm ≤ as < 180cm
Female Mode (Modal Group) = 155cm ≤ as < 170cm
From these answers I can see that the Year 11 Male modal Arm Span is 20cm ≤ as < 10cm longer than the Year 11 Female modal Arm Span, which is 11.42% ≤ as < 5.55% as a percentage.
4. Cumulative Frequency Graph
Here is the table and graph for Male Cumulative Frequency for Arm Span;
Here is the table & graph for Female Cumulative Frequency for Arm Span;
From these Cumulative Frequency Graphs I can see that the spread of the middle 50% of data for Males is slightly more than the spread of the data for Females. I can see that the median for females is a much lower length than the median for males. I can also clearly see that there are no females with a really long Arm Span, and no males have short Arm Spans.
5. Median
Male Median Arm Span = 176cm
Female Median Arm Span = 164.5cm
From these figures I can see that the Year 11 Male median Arm Span is 11.5 cm or 6.53% longer than the Year 11 Female median Arm Span.
6. Interquartile Range
Male Interquartile Range
= Q3 – Q1 = 182.5cm – 166.5cm = 16cm
Female Interquartile Range
= Q3 – Q1 = 170cm – 159cm = 11cm
Here are my Box and Whisker Diagrams for Arm Span;
From the Interquartile Range and Box and Whisker Diagrams for the Arm Span of Male and Female Year 11 Pupils I can see that the Inter quartile Range for Male Data covers longer lengths of Arm Span than the Female Interquartile range does. I can also see that the middle 50% of the data for males covers a larger amount of data than the female 50%.
7. Standard Deviation
Male Standard Deviation = 10.439
Female Standard Deviation = 7.599
From these figures I can see that the spread of the data for Arm Span around the mean is wider for Year 11 Males than it is for Year 11 Females, which can be clearly seen in the Box and Whisker Diagrams.
From all the calculations and graphs I have made for Male and Female Arm Span I have found out that on average Year 11 Males have between 5.55% and 11.42% longer Arm Spans than Year 11 Females.
4. The Average Year 11 Pupil
From all of the calculations and graphs I have made for the average Year 11 pupil I will now discuss the average Year 11 Pupil. I have found out that the average Year 11 Pupil will have a Height of between 165cm and 170cm, a Weight of between 55Kg and 62.59Kg, and an Arm Span of between 165cm and 170cm. I have also found out that I am not an average pupil; I have found out that I have a weight, height, and arm span which is between 8.0% and 19.1% larger than the average Year 11 Pupil.
5. Are Year 11 Pupils Square (All Data)
I will now try to find out if Year 11 Pupils are square. Below is my scatter diagram comparing height and arm span, with the data for all of Year 11;
From this Scatter Diagram I can see that the data does show a positive correlation, which means that there is a connection between height and arm span, and that Year 11 Pupils are almost square. There are some points which are outliers and do not fit the correlation, but I do believe that these data are genuine because I was there when the data was collected and not everyone will be square.
6. Are Year 11 Pupils Square (Male & Female Data)
I will now want to try and find out if Year 11 Males are squarer than Year 11 Females. Here are my two scatter diagrams for Male and Female data;
From these two scatter diagrams I can see clearly that the Heights and Arm Spans of the Female Pupils are smaller than the Height and Arm Spans of the Male Pupils. Both graphs show a very clear positive correlation, but the male data seems to have more outliers than the female data. The correlation for males seems to be longer and thinner and the correlation for females is shorter and wider. Overall I think that the female data shows the best correlation as the data is more tightly spread.
Conclusion
In this coursework I have found out that I am between 8.0 and 19.1% above the average weight, height, and arm span for a Year 11 pupil. I have found out that males have on average a longer arm span, and a bigger weight and height compared to an average Year 11 Male. And I have found out what the average Year 11 pupil would have for a height, weight, and arm span. I have also found out that height and arm span are connected and Year 11 pupils are square, and that female Year 11 pupils are squarer than male Year 11 pupils. For this coursework I collected 50 sets of data altogether and this was sufficient enough to get the answers and figures I needed to prove my hypothesis, and I have answered all of the things I wanted to answer in my hypothesis. I think that splitting the data into male and female to get two sets of figures and graphs to compare helped a lot to show the differences between the two sets of data. From the calculations and graphs which I did for my data I answered my hypothesis and on the whole my hypothesis was correct. If I did the coursework again I would take a bigger sample of data and see if the answers and figures I get are different. Almost all of the percentages I predicted in my hypothesis were correct. The purpose of this coursework was to find out the average year 11 pupil. I have found the average year 11 pupil using the data collected in my school, and used this to predict for the whole country (my prediction was an mean height of 169.832cm, a mean weight of 62.59Kg, and a mean arm span of 169.04cm. My prediction is limited due to the fact that I got my result from a small sample. I don’t expect my prediction to be perfect because the sample I took is probably too small to predict for the whole country, the sample was taken from my school only, the results might be biased because pupils in my school might be taller due to living next to the coast for example, and the data in my sample may not be quite accurate because I did not take these measurements myself. Overall I think I have been very successful in answering and proving my hypothesis, and I think I have given sufficient evidence to prove it correct.
If I was to do this coursework again I would take all of the measurements myself and measure them in the same way to make it fair. I would also take a larger set of data which would hopefully give more accurate results.