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  • Level: GCSE
  • Subject: Maths
  • Word count: 1580

Data handling coursework: Mayfield High School

Extracts from this document...

Introduction

Benjy Levey                 Data handling coursework

Data handling coursework: Mayfield High School

I have been given the data for 1183 students at a fictional school. The data is however not fictional. Different data is recorded for each student and ranges from their names, ages, height, weight, together with IQ, school results etc… I have chosen to investigate the relationship between height and weight. I think that this will be a more varied investigation unlike the relationship between eye colour and hair colour, as it is pretty random which colour eyes and hair you have and does not have anything in common.

 All the information given us is too much for us to use, and therefore I have selected only a small amount of data for each student, which will be relevant to the height and weight of each student.

As 1183 students are far too many to many to analyse correctly, I have taken ten people from each year group, five random boys and five random girls. First I sorted my data into years and gender and once they were separate I used the random number button on my calculator (ran# button)

...read more.

Middle

 (cm)

Tally

Frequency

120 ≤ h < 130

|

1

130 ≤ h < 140

0

140 ≤ h < 150

||||

4

150 ≤ h < 160

|||| ||||

9

160 ≤ h < 170

|||| |||

8

170 ≤ h < 180

||

2

180 ≤ h < 190

|

1

Weight, w (kg)

Tally

Frequency

20 ≤ w < 30

|

1

30 ≤ w < 40

||||

4

40 ≤ w < 50

||||||||||||

15

50 ≤ w < 60

||||

4

60 ≤ w < 70

|

1

70 ≤ w < 80

0

I will then show these tally charts above onto four separate bar graphs each relating to boys/girls height and weight.

image09.pngimage00.png

image01.png

image10.png

image04.png

image11.png

image05.png

image12.png

To make these graphs clearer to see, I will present the data in the form of two frequency polygon; one for girls and boys height, and one for girls and boys weight.

image06.png

image13.png

I can see from the frequency polygon that there are more girls with heights between 150 and 170cm than boys, but there are only a few more boys taller 170cm. This would suggest that possibly my hypothesis was not correct as there isn’t that much of a difference between boys and the girls.

image07.png

image14.png

This shows that the Boys’ data is more spread out than the girls. It also shows that there are fewer boys with weights between 20 and 60kg than girls. There are however more boys with weights higher than 60kg.

Averages for the data.

By looking at my frequency tables I will be able to determine what the mean, mode, median and range of all my data will be.  From discovering these, I will be able to determine whether my hypothesises were correct.  In order to find all these factors I will have to produce another frequency table.

Boys

 Height, h (cm)

frequency

midpoint

Fx = midpoint x frequency

130 ≤ h < 140

1

135

135

140 ≤ h < 150

2

145

290

150 ≤ h < 160

3

155

465

160 ≤ h < 170

6

165

990

170 ≤ h < 180

10

175

1750

180 ≤ h < 190

2

185

370

190 ≤ h < 100

1

195

195

∑f = 25

∑fx = 4195

...read more.

Conclusion

Girls

 Height, h (cm)

frequency

midpoint

fx = midpoint x frequency

120 ≤ h < 130

1

125

125

130 ≤ h < 140

0

135

0

140 ≤ h < 150

4

145

580

150 ≤ h < 160

9

155

1395

160 ≤ h < 170

8

165

1320

170 ≤ h < 180

2

175

350

180 ≤ h < 190

1

185

185

=

∑f = 25

∑fx = 3955

 The range in boys weights: 69 – 29 = 40kg

The mode for this data is: 140 ≤ h < 150.

The mean for this date is : x =         ∑fx = 3955 = 158.2

                                         ∑f          25 image03.pngimage02.png

The median for this data is: 150 ≤ h < 160

The range in girls’ heights is : 1.83 – 1.42 = 0.41m

girls

Weight, w (kg)

frequency

midpoint

fx = midpoint x frequency

20 ≤ w < 30

1

25

25

30 ≤ w < 40

4

35

140

40 ≤ w < 50

15

45

675

50 ≤ w < 60

4

55

220

60 ≤ w < 70

1

65

65

70 ≤ w < 80

0

75

0

=

25

1125

The mode of this data is: 40 ≤ h < 50.

The mean for this data is: x =         ∑fx = 1125 = 45

                                         ∑f          25 image02.pngimage03.png

The median for this data lies within the data is: 40 ≤ h < 50

The mean for this data is: x =         ∑fx = 1315 = 52.6

                                         ∑f          25 image03.pngimage02.png

The median for this data lies within the data is: 40 ≤ h < 50.

The range for girls’ weight is: 60 – 29 = 31

mode

mean

median

range

boys heights

70 ≤ h < 180

167.8

170 ≤ h < 180

0.57

boys weights

50 ≤ h < 60.

52.6

50 ≤ h < 60

40

girls heights

140 ≤ h < 150

158.2

150 ≤ h < 160

0.41

girls weights

40 ≤ h < 50

45

40 ≤ h < 50

31

I have discovered that, after working out the mean of both the boys’ and girls heights and weights, that in fact the both the boys height and weights are higher than the girls’.  This proves that my hypothesis is correct.

image15.jpg

Page

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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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