# GCSE Maths Coursework: Statistics Project

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Introduction

GCSE Maths Coursework: Statistics Project

The aim of this piece of coursework is to investigate the following hypothesis: ‘ In general, Year 10 girls are heavier and taller than year seven girls ‘ I am also going to investigate whether there is any correlation between height and weight. I have collected information from a computerized database that was given to me by my teacher. I have chosen these sources of information because there is a large quantity of data, it is reliable secondary data, and is easy to find. I know this data is reliable as I have sifted through any anomalies and crossed them off.

I have chosen to investigate a sample of 30 girls each year as it is large enough amount to get a fair result but small enough to manage. To ensure that it is a fair sample, I have picked out 30 girls at random, from the year seven and 10 group, by using the ‘ran button’ on a calculator. I will use this sample of data to compare the heights and weights of the year seven and 10 girls and to see whether my hypothesis is correct.

My chosen Data:

YEAR 7 GIRLS YEAR 10 GIRLS

Number of People | Height (cm) | Weight (kg) | Height (cm) | Weight (Kg) |

1 | 1.19 | 30 | 1.40 | 35 |

2 | 1.30 | 33 | 1.41 | 40 |

3 | 1.31 | 34 | 1.52 | 45 |

4 | 1.42 | 34 | 1.53 | 45 |

5 | 1.42 | 36 | 1.53 | 45 |

6 | 1.42 | 37 | 1.53 | 45 |

7 | 1.43 | 40 | 1.55 | 46 |

8 | 1.45 | 40 | 1.56 | 48 |

9 | 1.46 | 40 | 1.57 | 48 |

10 | 1.47 | 40 | 1.62 | 48 |

11 | 1.47 | 44 | 1.62 | 48 |

12 | 1.48 | 44 | 1.62 | 50 |

13 | 1.48 | 44 | 1.63 | 51 |

14 | 1.50 | 45 | 1.65 | 51 |

15 | 1.52 | 45 | 1.65 | 52 |

16 | 1.53 | 45 | 1.66 | 52 |

17 | 1.53 | 45 | 1.67 | 53 |

18 | 1.53 | 45 | 1.68 | 53 |

19 | 1.55 | 47 | 1.68 | 54 |

20 | 1.56 | 47 | 1.70 | 55 |

21 | 1.57 | 47 | 1.72 | 57 |

22 | 1.58 | 48 | 1.73 | 58 |

23 | 1.60 | 48 | 1.73 | 59 |

24 | 1.61 | 48 | 1.75 | 60 |

25 | 1.62 | 50 | 1.76 | 60 |

26 | 1.63 | 50 | 1.78 | 60 |

27 | 1.64 | 51 | 1.80 | 63 |

28 | 1.64 | 52 | 1.80 | 65 |

29 | 1.73 | 57 | 1.90 | 66 |

30 | 1.75 | 140 | 4.65 | 72 |

Representing my Data

Middle

45

1.53

45

1.53

45

1.55

46

1.56

48

1.57

48

1.62

48

1.62

48

1.62

50

1.63

51

1.65

51

1.65

52

1.66

52

1.67

53

1.68

53

1.68

54

1.70

55

1.72

57

1.73

58

1.73

59

1.75

60

1.76

60

1.78

60

1.80

63

1.80

65

1.90

66

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

Weights,w,kg | Tally | Frequency |

30<w<40 | \\\\ \ | 6 |

40<w<50 | \\\\ \\\\ \\\\ \\\\ | 19 |

50<w<60 | \\\\ | 4 |

60<w<70 | 0 | |

70<w<80 | 0 |

Year 10 girls Tally chart

Weights,w,kg | Tally | Frequency |

30<w<40 | \ | 1 |

40<w<50 | \\\\ \\\\ | 10 |

50<w<60 | \\\\ \\\\ \\ | 12 |

60<w<70 | \\\\ \ | 6 |

70<w<80 | \ | 1 |

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

Height,h,cm | Tally | Frequency |

110<h<120 | \ | 1 |

120<h<130 | 0 | |

130<h<140 | \\ | 2 |

140<h<150 | \\\\ \\\\ | 10 |

150<h<160 | \\\\ \\\\ | 9 |

160<h<170 | \\\\ \ | 6 |

170<h<180 | \\ | 2 |

180<h<190 | 0 | |

190<h<200 | 0 |

Year 10 girls Tally chart

Frequency Table

Height,h,cm | Tally | Frequency |

110<h<120 | 0 | |

120<h<130 | 0 | |

130<h<140 | 0 | |

140<h<150 | \\ | 2 |

150<h<160 | \\\\ \\ | 7 |

160<h<170 | \\\\ \\\\ | 10 |

170<h<180 | \\\\ \\ | 7 |

180<h<190 | \\ | 2 |

190<h<200 | \ | 1 |

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.

Heights (cm) | Mean | Modal Class Interval | Median | Range |

Year 7 | 1.46 | 140<h<150 | 1.53 | 0.56 |

Year 10 | 1.65 | 160<h<170 | 1.65 | 0.5 |

Conclusion

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.

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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