Pictogram: Basic diagrams which I predict will result in few marks and as the data is continuous it would be complicated to illustrate the data in pictures.
Tally Chart: The tally chart was substituted by the frequency table as it was more appropriate and it would show the same data.
Bar Chart: It was substituted by a histogram as the bar chart was basic and I believed the histogram was more appropriate for comparison instead of the bar chart.
Scatter Graph: This is inappropriate for my investigation as it is used to show two different sets of data on a graph to see if there is correlation or not. As I am only investigating girls weight with boys weight and girls height by boys height I am sure the results will not be suitable to prove the hypothesis.
Data Processing and Representing
Hypothesis 1- Boys weigh more than girls.
Boys Weight
In the weight column, means ‘26 up to but not including 36’. Any value greater than or equal to 26 but less than 36 would go in this class interval.
The weight of the boys’ is grouped in a class interval width of 10 Kg.
The frequency table shows the modal class interval is between 46 and 56 kg with a frequency of 11.
The cumulative frequency is similar to the frequency table however it shows the running total of all the class intervals. It shows the cumulative frequency double as it reaches the 46 and 56 Kg interval as this is because the frequency is highest for this interval.
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The stem and leaf diagram specifically shows the individual values of the weight of the 30 boys and the highest is 67 kg, lowest is 26 kg and the modal value is 40 kg.
The pie chart gives the percentage of the weight in the grouped class intervals and it visually creates the conclusion that the modal weight is between 46 and 56 kg as its percentage is 37.
The histogram above shows another visual diagram which easily forms the conclusion that
the modal weight of boys is in the 46 and 56 region.
The frequency polygon of the weight of boys’ show that the frequency decreases when the weight exceeds 51 kg as this indicates that not a lot of boys weigh more than 51 Kg. As this shows the frequency of boys starts to decrease as the weight starts to increase.
The Cumulative Frequency Curve above gives a much better visual concept of the lower quartile, median and the upper quartiles on the graph. The graph highlights the following,
Lower quartile: 40 Kg
Median: 49 Kg
Upper Quartile: 52 Kg
The box plot above shows no skewness this might be because of the extreme values affecting the whiskers of the box plot however the median is more reliable.
The box plot above states,
Lowest Value: 26 Kg
Highest Value: 67 Kg
Median: 49 Kg
The statistical calculations above show the following,
Average: The mean, median and modal class show a similarity and they basically give an idea of the average weight of boys throughout the year. This shows the average weight of a boy in the school is 48 Kg according to the mean weight.
Spread: The range shows a different value although it is affected by outliers or extreme values however the inter quartile range is not affected by these values.
The standard deviation shows the values of weight are 10.35 values away from the mean although this figure is quite significant this can’t be commented on as it hasn’t been compared with the standard deviation of the girls’ weight.
Girls Weight
The weight of the girls’ is grouped in a class interval width of 10kg and the most frequent weight is between 46 and 56 kg as the frequency for this is 18.
After this the frequency drops as the weight increases.
The cumulative frequency is similar to the frequency table however it carries on a running total of frequencies of all the class intervals. It indicates the cumulative frequency increase to 22 for the 46 and 56 class interval because the frequency for this class interval is 18.
The stem and leaf diagram specifically shows an individual value of the weight of 30 girls and the highest is 66 kg, lowest is 36 kg and the modal value is 52 kg.
The pie chart gives the percentage of the weight in the grouped class intervals and it visually creates the conclusion that the modal weight is between 46 and 56 kg as its percentage is 60.
This histogram shows a much easier visualisation of the fact that girls modal weight is between 46 and 56 kg.
The frequency polygon above indicates that the frequency starts to decrease as the weight starts to exceed 51 kg. This shows not a lot of girls weigh more than 51 kg.
This cumulative frequency graph shows all the quartiles on the graph as well as the median.
It shows the following,
Lower Quartile: 47 Kg
Upper Quartile: 55 Kg
Median: 52 Kg
The box plot of girls’ weight shows no skewness as the Range is 30 which is the same as the number of girls. The box plot shows the following,
Highest Value: 66 Kg
Lowest Value: 36 Kg
Median: 52 Kg
The statistical calculations above show the following,
Average: The mean, median and modal class show a similarity and they basically give an idea of the average weight of girls throughout the year. This shows the average weight of a girl in the school is 52 Kg according to the mean weight.
Spread: The range shows a different value although it is affected by outliers or extreme values however the inter quartile range is not affected by these values.
The standard deviation shows the values of weight are 6.677 values away from the mean although this figure is quite significant this can’t be commented on as it hasn’t been compared with the standard deviation of the boys’ weight.
Comparison
Girls weight Boys Weight
Comparing the stem and leaf diagram I can identify that the modal weight of girls is 52 Kg and for the boys its 40 kg. Thus this result goes against the hypothesis as it shows a significant difference of 12 Kg.
This proves my hypothesis wrong as it shows that the average modal weight of girls is higher than boys.
The highest value is of the boys by only 1 Kg as this shows the minimum spread and it can’t be commented upon until further investigation.
The lowest value of girls is 10 Kg more than boys so this again goes against the hypothesis as the minimum weight is of boys is 10 Kg less than the girls.
The histogram of the boys and girls weight illustrates that the girls frequency of class intervals is mostly higher than boys especially for the modal 46kg class interval or are equal with the boys and this shows that girls mostly weigh more than boys thus in turn proves the hypothesis wrong.
The cumulative frequency curve above shows the following,
It illustrates the fact that boys quartiles and median is lower than girls’ this goes on to disapprove my hypothesis and proves that girls weigh more than boys on average.
The box plots above show the following,
This goes on to prove that although no comparison of skewness, all the girls values are higher than the boys and this obviously shows the girls weigh more than boys on average.
Comparing the averages, quartiles and spread of the boys and girls weight I can conclude that the girls’ averages are higher than boys so this mainly proves my hypothesis wrong as I can successfully state that girls weigh more than boys in all the year groups. Their standard deviation is much lower as this shows that the values from the mean average are much closer than of the boys. This shows that girls’ weight is much consistent and closer than of the boys.
Summary
To summarise in most comparisons it has been illustrated that altogether girls weigh more than boys in all year groups.
This statement is based on the comparison of averages and quartiles, standard deviation, spread and the highest values and lowest values.
Hypothesis 2 - Boys are taller than girls.
Boys Height
The boys frequency table above shows the most frequent height is in between 162 -172 cm with a frequency of 11. The height of the boys’ is grouped in a class interval width of 10 cm.
The cumulative frequency table is similar to frequency table although it shows a running total of the frequencies and shows like the frequency table that the modal height is between 162 and 172 cm.
The stem and leaf diagram above shows all the individual heights for the 30 boys and the highest height is 184 cm and lowest is 142 cm and the modal value is 165 cm.
The pie chart gives the percentage of the weight in the grouped class intervals and it visually creates the conclusion that the modal height is between 162 and 172 cm as its percentage is 37.
The histogram above visualises the fact that the modal height is in between 162 – 172 cm.
The frequency polygon above indicates that as the height exceeds the modal height of 167 cm, the frequency decreases as the heights get higher.
The cumulative frequency diagram above couldn’t present median, upper quartiles and lower quartiles because of an error on the data handling tool.
The box plot above shows a positive skewness this might be because of the extreme values affecting the whiskers of the box plot however the median is more reliable.
The box plot above states,
Lowest Value: 142 cm
Highest Value: 184 cm
Median: 162 cm
The statistical calculations above show the following,
Average: The mean, median and modal class show a similarity and they basically give an idea of the average height of boys throughout the year. This shows the average height of boys in the school is 162 cm according to the mean height.
Spread: The range shows a different value although it is affected by outliers or extreme values however the inter quartile range is not affected by these values.
The standard deviation shows the values of height are 10.753 values away from the mean although this figure is quite significant this can’t be commented on as it hasn’t been compared with the standard deviation of the girls height.
Girls Height
The frequency table above suggests that the modal class interval is 150 to 160 cm by a frequency of 14.
The cumulative frequency shows the running total increase significantly as it reaches the class interval of 150 to 160 cm as this is the modal height.
The stem and leaf diagram above shows the individual values of the heights of all thirty girls and shows the following,
Lowest Value: 140 cm
Highest Value: 175 cm
Modal Value: 155 cm
The pie chart above illustrates the modal class interval at 47% for the 150 and 160 cm class as this is the most frequent class.
The histogram illustrates the modal height in the class interval 150 to 160 cm with a frequency of 14.
The frequency polygon above indicates that as the height exceeds the modal height of 155 cm, the frequency decreases as the heights gets higher.
The cumulative frequency curve above couldn’t present median, upper quartiles and lower quartiles because of an error on the data handling tool.
The box plot above shows an unnoticeable positive skewness, this might be because of the extreme values affecting the whiskers of the box plot however the median is more reliable.
The box plot above states,
Lowest Value: 140 cm
Highest Value: 175 cm
Median: 158 cm
The statistical calculations above show the following,
Average: The mean, median and modal class show a similarity and they basically give an idea of the average height of girls throughout the year. This shows the average height of girls in the school is 159 cm according to the mean height.
Spread: The range shows a different value although it is affected by outliers or extreme values however the inter quartile range is not affected by these values.
The standard deviation shows the values of height are 7.924 values away from the mean although this figure is quite significant this can’t be commented on as it hasn’t been compared with the standard deviation of the boys height.
Comparison
Girls weight Boys Weight
Comparing the stem and leaf diagram I can identify that the modal height of boys is 165 cm and for the girls its 155 cm. Thus this result goes against the hypothesis as it shows a significant difference of 10 cm.
This proves my hypothesis right as it shows that the average modal height of boys is higher than girls.
The highest value is of the boys by 11 cm as this shows another significant difference and shows the tallest boy is 11 cm taller than the tallest girl.
The lowest value of girls is 2 cm less than boys so this again goes for the hypothesis but it will be disregarded as the spread is by only 2cm.
The histogram of the boys and girls height illustrates that the girls frequency of class intervals is lower than boys especially for the modal class interval or are equal with the boys and this shows that girls mostly smaller than boys based on the average and it proves my hypothesis right.
The comparative frequency curve could not be drawn because of an error on the data handling tool.
The box plots above show the following,
This goes on to prove that although boys have a higher positive skewness, all the girls values are lower than the boys and this obviously shows that girls are smaller than boys on average.
This successfully proves my hypothesis.
* There was an error above in the summary standard deviation as it was different.
Comparing the averages, quartiles and spread of the boys and girls weight I can conclude that the boys’ averages were higher than girls so this mainly proves my hypothesis right as I can successfully state that boys are taller altogether than girls. Their standard deviation is much higher as this shows that the values from the mean average are much spread out than of the girls. This shows that girls’ height is much consistent and closer than of the boys.
Summary
To summarise in most comparisons it has been illustrated that altogether boys are taller than girls.
This statement is based on the comparison of averages and quartiles, standard deviation, spread and the highest values and lowest values.
Conclusion
Looking at the above evidence of the graphs, tables, calculations and interpretations I can successfully say that it doesn’t prove any of my theories because the results are bias as I only take into account one school.
The sample was too small and the data collected in my opinion didn’t represent the population.
If I was to do the investigation again I would have done the graphs and calculations by other means instead of the software provided by Edexcel which in my opinion was unreliable as it had errors, inappropriate diagrams as well as minimum options from which I could have specifically changed the diagrams.
The investigation could be developed further by taking into account a bigger population and comparing it with another school.
However the hypothesis I have proven for this school is the fact that boys are taller than girls altogether but girls weigh more than boys altogether.