# Data Handling Maths Coursework

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Introduction

Mathematics GCSE Coursework Roshni Sharma

MATHEMATICS

GCSE COURSEWORK

Data Handling Investigation

Roshni Sharma

Centre Number:

Candidate Number:

Contents

INTRODUCTION

Aims 3

Hypotheses 3

Variables 4

Sampling 4

Plan 6

Common Terms 6

Random Samples 7

DATA PROCESSING & INTERPRETING

1ST Hypothesis 12

2ND Hypothesis 16

3RD Hypothesis 20

4TH Hypothesis 22

EVALUATION

Conclusion 27

Limitations 28

Introduction

In this investigation, I am looking at a mixed, secondary school called Mayfield High School. I am going to be looking at the students in key stage three and key stage four. I do not have any knowledge about the details of this school, for instance, its location.

Mayfield is a fictitious school but the data presented is based on a real school. I obtained the data about the school from an electronic database. This is a secondary source of information, as I have not obtained this data myself. If I was to have done the research and obtained the data for myself, I would have given questionnaires to all the pupils and asked them relevant questions in relation to what I want to study.

The total number of students at the school is 1183.

Aims:

To investigate the way height and weight of boys and girls change with their age. I also intend to investigate the relationship between height and weight, how they affect each other and the patterns that they follow.

Hypotheses:

- Most girls are taller than boys in year 7

I have chosen to investigate this hypothesis, as I think there will be a significant height difference between girls and boys in year 7. I know from scientific knowledge that in year 7, many girls have already hit puberty- they have already begun to grow and develop; the average age that girls begin to mature is between 8 and 13. This age group falls in key stages 2 and 3.

Middle

Maximum height (cm)

Median Height

(cm)

Mean Height

(cm)

Modal Class Interval

(cm)

Girls

58

119

180

148

154

150≤ h <160

Boys

67

119

175

149

155

150≤ h <160, 160≤ h <170

The frequency polygon shows frequencies of heights; it compares the heights of boys and girls in year 7. There are a few boys and girls in year 7 who, in terms of height, are between [110cm and 140cm], which are the lowest heights, and [170cm and 190cm], which are the highest heights. The majority of people in year 7 lie between the values of 140cm and 170cm. This means that height in year 7 generally follows normal distribution. The line for the girls in year 7 peaks at the same height as boys in year 7, although the line for boys peaks through two intervals. The frequency for the modal class interval for girls is lower than frequency for the modal class interval for boys; when 150cm ≤ h < 160cm, there are 21 girls and 22 boys, and when 160cm ≤ h < 170cm, there are only 12 girls but 22 boys.

The graph shows that generally, boys in year 7 are taller than girls in the same age group. This can be seen because the pink line for girls runs below the blue line for boys. This means that the frequency at each class interval is less for girls than for boys. The minimum height for both girls and boys is the same: 119cm. However, the maximum height is higher for girls: 180cm. This is unusual, seeing as all the other data shows that boys are taller than girls. The mean, median and modal heights are higher for boys. However, these results may not be 100% reliable, because there is one important limitation of this data: the sample sizes for the boys and the girls in year 7 are different. The sample that was taken for boys is bigger than the sample taken for girls. This means that the boys’ study was done in more detail because there were more samples, and therefore the frequencies are higher. If the girls had more samples, the frequencies for the girls may have been higher.

The averages for boys are higher than for girls. Using standard deviation, I am going to work out the spread of the data.

Standard Deviation:

Table displaying data of girls in year 7

Height (cm) | Frequency f | Mid-point x | Frequency x Midpoint fx | Frequency x Midpoint² fx² |

110 ≤ h < 120 | 1 | 115 | 115 | 13225 |

120 ≤ h < 130 | 1 | 125 | 125 | 15625 |

130 ≤ h < 140 | 2 | 135 | 270 | 36450 |

140 ≤ h < 150 | 18 | 145 | 2610 | 378450 |

150 ≤ h < 160 | 21 | 155 | 3255 | 504525 |

160 ≤ h < 170 | 12 | 165 | 1980 | 326700 |

170 ≤ h < 180 | 2 | 175 | 350 | 61250 |

180 ≤ h < 190 | 1 | 185 | 185 | 34225 |

Totals: | 58 | 8890 | 1370450 |

Table displaying data of boys in year 7

Height (cm) | Frequency f | Mid-point x | Frequency x Midpoint fx | Frequency x Midpoint² fx² |

110 ≤ h < 120 | 4 | 115 | 460 | 52900 |

120 ≤ h < 130 | 2 | 125 | 250 | 31250 |

130 ≤ h < 140 | 2 | 135 | 270 | 36450 |

140 ≤ h < 150 | 12 | 145 | 1740 | 252300 |

150 ≤ h < 160 | 22 | 155 | 3410 | 528550 |

160 ≤ h < 170 | 22 | 165 | 3630 | 598950 |

170 ≤ h < 180 | 3 | 175 | 525 | 91875 |

180 ≤ h < 190 | 0 | 185 | 0 | 0 |

Totals: | 67 | 10285 | 1592275 |

Standard deviation is a measure of spread; it can tell you how spread out the data in a set are from its mean. The standard deviation is the square root of the variance, where µ represents the mean of the data and N represents the number of samples. Before the standard deviation is worked out, it is necessary to know the frequencies, mid-points, and products of them both, of all the sets of data. The following formula is used to work out standard deviation:

0² = ∑ (x - µ) ²

N

Standard deviation for girls= 11.62 (2dp)

Lower Bound=142.38

Upper Bound=165.62

Standard deviation for boys= 14.17 (2dp)

Lower bound = 140.83

Upper bound = 169.17

My results told me that the standard deviation for boys is higher than the standard deviation for girls. Standard deviation is the dispersion of a set of data from its mean. The higher the number of standard deviation is, the larger the spread of the data. Therefore my results tell me that the data for the boys is more spread out than the data for the girls. The lower bound is lower for boys than for girls, and the upper bound is higher. This tells me that the majority of the boys lie in a wider spread of data, whereas the girls are concentrated in a smaller spread.

Conclusion:

My graphs and results tell me that my hypothesis is incorrect. I predicted that girls would be taller than boys in year 7; however my results proved the opposite. I did not expect this to happen, as I had initially stated this hypothesis after doing some background research on the heights of girls and boys as they grow up. The unforeseen outcomes my have been a result of inaccurate sampling or data. Furthermore, the limitations of this investigation could have had an effect on it, such as the different sample sizes (mentioned previously, page 13).

2.Most Boys are Taller than Girls in Year 11

For my second hypothesis, I used the other half of my sample from the other two strata, girls in year 11 and boys in year 11. To prove my hypothesis, I had to present the data in the same way as for my first one, to compare the heights of the girls and the boys in year 11. I therefore, created a frequency polygon.

I used the same method as I did for my first hypothesis, working out the intervals, sorting the data and plotting the graph. The table below shows the frequencies and mid-points for the heights of girls and boys in year 7.

Height (cm) | Frequency of Girls | Frequency of Boys | Mid-point (cm) |

110 ≤ h < 120 | 0 | 0 | 115 |

120 ≤ h < 130 | 0 | 0 | 125 |

130 ≤ h < 140 | 1 | 1 | 135 |

140 ≤ h < 150 | 0 | 0 | 145 |

150 ≤ h < 160 | 10 | 8 | 155 |

160 ≤ h < 170 | 21 | 11 | 165 |

170 ≤ h < 180 | 6 | 6 | 175 |

180 ≤ h < 190 | 0 | 5 | 185 |

190 ≤ h < 200 | 0 | 4 | 195 |

200 ≤ h < 210 | 0 | 2 | 205 |

38 | 37 |

Averages:

Number of samples/ total frequency | Minimum height (cm) | Maximum height (cm) | Median Height (cm) | Mean Height (cm) | Modal Class Interval (cm) | |

Girls | 38 | 137 | 176 | 163 | 162 | 160 ≤ h < 170 |

Boys | 37 | 132 | 203 | 168 | 172 | 160 ≤ h < 170 |

Conclusion

My investigation was generally successful, as I found my hypotheses were mostly correct. To improve my investigation, I could have used a wider range of samples, as a larger amount of data makes analysis more reliable. Using more samples means my data will be more representative of the results and therefore more accurate.

Limitations:

The main limitation of my investigation was my methods, sizes and results of my sampling. At times, when I was making comparisons between two strata, I found that the sample sizes for each were different. This made it difficult to make comparisons, as I knew the processes data and graphs were not 100% reliable, as the samples were bias. Additionally, I found that I had only sampled two out of five year groups in the whole school. Therefore, when I was making comments about the entire population, I knew my comments would be based on bias data, because I only have values from two year groups.

Anomalous results were another limiting factor for my investigation. I tried to pick out and remove any anomalies or outliers from my data. However, this was no always possible and therefore, these values could have had an effect on the patterns that the graphs and data showed. Mistypes in the database provided anomalous results. These were human errors which caused the limitations. I got around this problem by re-sampling if obtained a sample which had an error.

Obviously, not each and every student will fit the pattern, each individual will vary. Height and weight is affected by a number of different variables, not only age and gender. For instance, other variables which may affect height and weight are hours spent watching television, or means of transport to school. These variables affect height and weight indirectly because they are more to do with lifestyle. Therefore, we can not definitely get to the bottom of each anomaly.

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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