# Identify patterns that emerge from groups of data in girls and boys heights and weights.

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Introduction

Maths Coursework

By Arun Joshi

Aim:

The aim of this coursework is to identify patterns that emerge from groups of data, such as, ‘this weight will mean that this height will be…’ In this work I shall be looking at grouped data in girls and boys heights and weights.

Firstly I should collect 30 random samples of data from a table, since there are 604 boys and 579 girls (all together 1183 pupils), so we should…

- 1184 Pupils ∴ Random X 1184 = Generated Number.

- When you get this Generated Number you look this up in a table, which will give you a name, height and weight of the pupil.

- Then do this 30 times and provide it in a table…

Number | Height (cm) | Weight (kg) |

127 | 148 | 37 |

414 | 150 | 39 |

633 | 152 | 50 |

181 | 160 | 56 |

419 | 165 | 45 |

182 | 156 | 35 |

860 | 141 | 35 |

427 | 162 | 49 |

537 | 160 | 43 |

332 | 154 | 54 |

1148 | 157 | 54 |

4 | 130 | 36 |

28 | 159 | 41 |

241 | 159 | 49 |

6 | 160 | 42 |

42 | 154 | 42 |

326 | 162 | 46 |

722 | 150 | 70 |

104 | 163 | 50 |

1126 | 182 | 66 |

996 | 168 | 64 |

467 | 186 | 58 |

702 | 180 | 48 |

1048 | 159 | 45 |

1074 | 161 | 45 |

770 | 161 | 60 |

787 | 150 | 39 |

1097 | 169 | 50 |

796 | 174 | 61 |

2 | 142 | 34 |

As you can see we get this result. Which is no good if we cannot understand it, since its complete ‘mumbo-jumbo’ to the normal eye. Well to the trained eye you can see the important areas of these results.

- Height in cm, of which the highest is 186cm, and the lowest, is 130cm.
- Weight in kg, of which the highest is 70kg, and the lowest is 34kg.

Excellent but this isn’t all we must arrange the data so we can look at it easily, so the best way is the old fashioned ‘tally’ method.

Height (cm) | Tally | Frequency |

130 ≤ h < 140 | I | 1 |

140 ≤ h < 150 | III | 3 |

150 ≤ h < 160 | IIII IIII I | 11 |

160 ≤ h < 170 | IIII IIII I | 11 |

170 ≤ h < 180 | I | 1 |

180 ≤ h < 190 | II | 3 |

As you can plainly see, this is a tally table for the heights of the 30 randomly chosen values, except they are in a table with intervals in them. In this case it is a 10cm interval gap.

Weight (kg) | Tally | Frequency |

30 ≤ w < 40 | IIII I | 6 |

40 ≤ w < 50 | IIII IIII I | 11 |

50 ≤ w < 60 | IIII III | 8 |

60 ≤ w < 70 | IIII | 4 |

70 ≤ w < 80 | I | 1 |

This is the table for the weights of the 30 randomly chosen individuals. Also as the tally before there is an interval of 10, which is appropriate later on when we make the graphs.

Well as mentioned in the paragraph above ‘later’ is ‘now’. The graphs I am making resemble the tally data in histogram form, which is excellent for this area of working!!!

Now as you can see I have made the graphs which identifies the height and weight over the 30 random pupils. What I have noticed already is that the height data values are not as proportionate as the weight values, funny isn’t it? This was probably due to the generated numbers picking the values, which are nearer the higher end of the value sheet first given to me!!!

Amazing isn’t it, well the last thing we must do with these values is plot it against each other, the best way to plot height against weight is the ‘scatter diagram’.

Well your probably thinking to yourself now, “This is GREAT, where does Ross get this stuff?” The scatter diagram, which is plotted above, shows the data of height and weight plotted against each other. The main trend here is a positive correlation, apparent from the data increasing in accordance to each other.

However just having these data values is not just enough, it doesn’t prove anything from the data I have just retrieved. So we have to go one step further to get proof that an equation of ‘some sort’ exists that proves the relation in the height and weights of pupils.

Firstly, I will start with exactly the same method I put to action at the beginning of this coursework. Since the values in the last one consisted of both male and female values we must work to the standards of two values. Lets say for example that the values from the first table were just too many to pick out values of boys and then the girls, separately and slowly, utilising the random method. WE WOULD BE HERE UNTIL CHRISTMAS 2003!!! So by common sense I was given two separate sheets, one with the male height and weight values and the other with the female height and weight values.

## Random Student Averages

Mean values:

- Height 154.4 cm
- Weight 72.3 kg

Height Values (cm) smallest value first:

130,141,142,148,150,150,150,152,154,154,156,157,159,159,159,160,160,160,161, 161,162,162,163,165,168,169,174,180,182,186.

Weight Values (kg) smallest value first:

34,35,35,36,37,39,39,41,42,42,43,45,45,45,46,48,49,49,50,50,50,54,54,56,58,60,61, 64,66,70.

Modal Class: Height: 150 ≤ h < 160, 160 ≤ h < 170

Weight: 40 ≤ w < 50

Median | = | 30 + 1 / 2 | ∴ | Height | = | 159.5 |

∴ | Weight | = | 47 | |||

Lower Quartile | = | 30 + 1 / 4 | ∴ | Height | = | 151 |

∴ | Weight | = | 40 | |||

Upper Quartile | = | 3 X (30 + 1) / 4 | ∴ | Height | = | 164 |

∴ | Weight | = | 55 |

As you can see these are the data I collected and put into a graph. It shows the averages, median, upper and lower quartiles as well as the modal classes.

## Random Girls and Boys

Firstly I should collect 30 random samples of data from a table, since there are 604 boys and 579 girls (all together 1183 pupils), we should…

- 604 Boys ∴ Random X 604 = Generated Number.

579 Girls ∴ Random X 579 = Generated Number.

- When you get this Generated Number you look this up in the relevant table, which will give you a name, height and weight of the males and females.

- Then do this 30 times and provide it in two tables…

## Female Values

...read more.Middle

68

160

38

488

165

68

133

150

34

351

174

57

537

173

50

536

167

50

445

157

64

51

156

35

385

170

37

324

160

70

28

158

48

202

134

32

451

177

72

304

180

42

109

150

40

440

177

57

149

162

52

340

162

62

378

172

90

353

144

49

489

155

72

564

200

86

408

180

55

597

179

72

565

197

84

477

189

64

118

153

44

587

193

46

These are the male values present by multiplying 604 by a random number, which is considerably easier if you use the calculator’s random key.

As you may of noticed you also get these results, which are needed to get us going onto the next area of working.

The female values prove that in the area of height, the highest is 180cm and the lowest is 120cm and the heaviest weight in kg was 67kg while the lightest female is weighed in at 38kg.

The same very much applies to the male rule, in the area of height the highest is 200cm and the shortest is 134cm, and in the area of mass the heaviest was 90kg while at a measly 35kg it proved to be the lightest.

So now we have found the height and weight values of both the males and the females. The next area that we must delve into now is the process of tallying the data into an easy-to-read graph, but first we must tally the data…

Firstly the females…

Number | Height (cm) | Weight (kg) |

60 | 155 | 50 |

245 | 133 | 45 |

435 | 157 | 60 |

176 | 160 | 51 |

577 | 169 | 50 |

541 | 170 | 60 |

301 | 156 | 38 |

556 | 162 | 51 |

64 | 162 | 40 |

324 | 120 | 42 |

522 | 152 | 48 |

Height (cm) | Tally | Frequency | Cumulative Frequency |

120 ≤ h < 130 | I | 1 | 1 |

130 ≤ h < 140 | I | 1 | 2 |

140 ≤ h < 150 | I | 1 | 3 |

150 ≤ h < 160 | IIII IIII | 10 | 13 |

160 ≤ h < 170 | IIII IIII I | 11 | 24 |

170 ≤ h < 180 | IIII | 5 | 29 |

180 ≤ h < 190 | I | 1 | 30 |

Weight (kg) | Tally | Frequency | Cumulative Frequency |

30 ≤ w < 40 | II | 2 | 2 |

40 ≤ w < 50 | IIII IIII | 10 | 12 |

50 ≤ w < 60 | IIII IIII III | 13 | 25 |

60 ≤ w < 70 | IIII I | 5 | 30 |

As you can see (obviously you can…duh!), it shows the tally of the female weights and heights, of 30 random females.

Now for the males…

Height (cm) | Tally | Frequency | Cumulative Frequency |

130 ≤ h < 140 | I | 1 | 1 |

140 ≤ h < 150 | I | 1 | 2 |

150 ≤ h < 160 | IIII III | 8 | 10 |

160 ≤ h < 170 | IIII I | 6 | 16 |

170 ≤ h < 180 | IIII II | 7 | 23 |

180 ≤ h < 190 | III | 3 | 26 |

190 ≤ h < 200 | III | 3 | 29 |

200 ≤ h < 210 | I | 1 | 30 |

Weight (kg) | Tally | Frequency | Cumulative Frequency |

30 ≤ w < 40 | IIII | 5 | 5 |

40 ≤ w < 50 | IIII III | 8 | 13 |

50 ≤ w < 60 |

Conclusion

As with all the cumulative frequency diagrams there is also the weight factor which in this area is as important as the height. With a VERY GOOD REASON. As you can see from the graph the female trend seemed to stop in the regions of 60 kg, this proposes to us that the weight ended simply because it reached its highest value. On the other hand the male values continued to a much later weight in the area of 90kg, obviously stating that it too also had a maximum weight, much like the females abrupt low value. Meanwhile if you look at the trend, the female are considerably heavier in one region of weight, compared to the boys, which show a lower trend. The female’s rise steeply, showing the large numbers, while the males remain evenly distributed in frequency as the weight rises. The combined value shows the trend, which I was explaining above, in more detailed fashion, the cumulative frequency rose steeply in almost the same fashion as the females and from there on evened out.

This whereby shows the weight and height distribution in both males and females.

Now I shall be making my ‘Box Plot’ diagrams…

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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