In comparison to the scatter diagram for the year seven girls, this graph shows that year 10 girls are generally taller. I can see this as the height of the year 10 girls starts at 1.4cm whereas the year seven girls start at 1.2 cm.
The scatter diagram above shows that there is strong positive correlation between the Height and Weight of Year 10 girls, illustrating that the taller you are the more heavy you tend to be.
The year tens are obviously, and are bound to be, taller than the year sevens as they are older. This evidence supports my hypothesis that ‘In General, Year 10 girls are heavier than year seven girls.
The table on the left shows the data needed to do the scatter diagram. The data is of the Year 10 girl’s height and weights.
This scatter diagram proves that Year 10 girls are taller than Year 7 girls. The diagram shows this as the pink squares, which are the Year tens, are at a higher level than the year sevens. Therefore, they are taller than the younger year. This is not surprising as the older we get the more tall we are.
This scatter diagram has much the same purpose as the graph before, except this graph shows relation between the weights of the two year groups. From looking at the graph, I can see that the Year 10 girls are heavier than the year sevens. From the previous scatter diagrams I have seen that there is strong correlation between height and weight meaning that the Year 10’s are bound to be heavier.
WEIGHTS
Year 7 girls Tally chart
Year 10 girls Tally chart
These frequency tables are a more simple way of presenting data. They help me to see the most common class intervals.
Here are Bar Charts to show this data:
This bar chart illustrates the data in the frequency tables. The chart shows that the modal class interval for weight is 40 <w <50 for the Year 7 girls. This graph shows that a majority of the Year 7’s are between 40 < w < 50 and therefore, a majority are likely to be average weight.
This bar chart shows that the modal class interval for weight is 50<w<60 kg for the year 10 girls. The bar chart shows that not many people weigh between 30<w<40 and 70<w<80, probably because these intervals are said to be underweight and overweight. From looking at this bar chart I can see that the average weight is 50<w<60.
This frequency polygon shows the comparison between the two year groups. The year 7 girls clearly weigh less. I can see that none of the girls in Year 7 weigh over 60kg. The modal class interval for the year tens is between 50<w<60kg which is clearly the average. By looking at this frequency polygon, I can see that the year ten girls are more widely spread than the younger year. The year sevens have a more steep line; the steepest point is at 40<w<50.
Heights
Year 7 girls Tally chart,
Frequency Table
Year 10 girls Tally chart
Frequency Table
Bar charts to show these results are on the following page:
The Bar graph reflects where the modal class interval is. For the year sevens, the modal class interval is 140 <h<150 cm. The graph shows that not many people are more than 170cm. A majority of the year seven girls are between 140<h<170 cm.
This bar chart shows that a majority of the year tens are quite tall and are further up in the scale than the year sevens. The modal class interval is 160<h<170 which is average height. In comparison to the year sevens, the year tens are much taller. This can be proven in the above bar charts.
I have used a Dual Bart Chart to make it easier to compare the two years. By referring to the bar chart above, I can see that the year sevens are generally shorter than the year tens, which again supports my hypothesis.
Averages
I am now going to record the mean, median and range for the data. Because weight and height are continuous data, it makes more sense to find the modal class interval rather than the mode. This is the class interval that contains the most values. The tables above both show what the modal class intervals are. I have decided to round the values for the mean and median to two decimal places as I feel it is easier to recall.
The table above shows that the year tens are generally taller than the year sevens. The modal class for the year tens is between 160<h<150 whereas the year sevens have a modal class interval of 140<h<150. However, the sample for the year sevens is more spread out with a range of 0.56cm, compared to 0.5cm for the year tens. To conclude, clearly year tens are taller than the year sevens. This is probable seeing as children grow as they get older.
The table is useful to me as it proves that year tens generally weigh more than the year sevens. For the year tens, the modal class interval is 50<w<60 whereas the modal class interval for the year sevens is 40<w<50. Graphs earlier have proved that the taller we get, the more we tend to weigh. The table above also shows that the year tens are more spread out with a range of 37kg, which is in contrast to the averages above of heights.
Stem and Leaf diagrams:
I have chosen to do some stem and leaf diagrams as they will be useful in helping me to compare the two years, and will help me to see what the most common height is.
YEAR 7 GIRLS HEIGHT, CM
From looking at the above Stem and Leaf diagram, I can see that 1.4cm and 1.5cm are the most common (mode). Also, I can see that not many people are taller than 1.6 cm or are shorter than 1.4 cm.
YEAR 10 GIRLS HEIGHT, CM
From looking at this Stem and Leaf diagram, I can see that the mode is 1.6 cm. This diagram also helps me to see that the average height for the year is between 1.5 and 1.7 cm. Furthermore, the diagram helps me to see that not many people are over 1.7cm.
From studying both Stem and Leaf diagrams, it becomes clear that the year tens are taller. I can see this as their minimum height is 1.4cm which is a few centimeters more than Year 7. In addition, the Year 7s most common class interval is 1.4cm<h<1.5cm where as for the year tens, the modal class interval is 1.6cm<h<1.7cm.
YEAR 7 GIRLS WEIGHT, KG
This stem and leaf diagram shows that the modal weight is 45kg. The modal class interval is clearly 40kg<w<50kg. From looking above, I can see that a majority of my random sample in year seven weigh between 30 - 40 kg. This stem and leaf diagram also shows that no one weighs more than 60kg.
YEAR 10 GIRLS WEIGHT, KG
This stem and leaf diagram shows that the modal class interval for the year tens is 50 <w<60 kg. A majority of the year 10 sample weigh between 40 – 60 kg. Not many weigh more than 70kg, or less than 40kg.
Clearly, the year tens are heavier than the year sevens. This is evident as the modal class interval is 40<w<50kg, whereas the year tens’ modal class interval is 50<w<60kg. Therefore, they tend to weigh more.
Cumulative Frequency
I am going to draw cumulative frequency curves in order to compare the two years. Also, with a cumulative frequency curve I can easily read off the median, upper quartile, lower quartile and interquartile range.
Weight
This cumulative frequency curve is very useful as I can now find out the median, upper quartile, lower quartile and interquartile range:
This is more accurate data, is it is a continuous approximation of the distribution of values. From these results, I can see that the year tens have a higher median and have more interquartile range. This means that there is a wider spread of data for the year tens – their weight ranges more than the year sevens.
Height
From this, I can now find out the median, upper quartile, lower quartile and interquartile range:
This table proves that generally, year tens are taller than the year sevens. In comparison to the weights, the year tens have a large Interquartile range.
I can use this information that I have read from the cumulative frequency curves to draw box- and- whisker diagrams, showing the minimum and maximum values, the median, and the upper and lower quartiles:
Box and Whisker Diagrams for height:
Box and Whisker Diagrams for weight:
Conclusion
Now that I have investigated the height and weight of each year, I can now see whether my hypothesis is correct. I have presented my information and now have enough evidence to say that my hypothesis is accurate. It is true that in general year ten girls are heavier and taller than year seven girls - this can be supported with evidence. It has become clear throughout my piece of coursework that year tens are heavier and taller than year seven girls as they are older. As we grow up, we tend to grow. It is evident that the taller we get, the heavier we are. A scatter graph earlier in the piece of coursework proves this as there is strong, positive correlation.
Overall, I am pleased with how this piece of coursework has gone. The investigation has gone well and I have made evidence to prove that generally, year ten girls are heavier and taller than year seven girls. If there were any changes to be made and if I had more time, I would extend my investigation and provide more solid evidence. However, on the positive side, I have been pleased with my achievements; I have investigated my hypothesis in depth and have provided solid evidence to back up this investigation.