• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month
Page
1. 1
1
2. 2
2
3. 3
3
4. 4
4
5. 5
5
6. 6
6
7. 7
7
8. 8
8
9. 9
9
10. 10
10
11. 11
11
12. 12
12
13. 13
13
14. 14
14
15. 15
15
16. 16
16
17. 17
17
18. 18
18
19. 19
19
20. 20
20
21. 21
21
22. 22
22
23. 23
23
24. 24
24
• Level: GCSE
• Subject: Maths
• Word count: 3541

# I am going to use secondary data for my investigation on comparing height and weight of school children.

Extracts from this document...

Introduction

I am going to use secondary data for my investigation. I have acquired my data from the website www.mathsmatrix.co.uk. The data is based on a real school but the name of the students and the school has been changed. The data is presented as a single list of 1183 pupils, from year 7 to year 11. I have chosen to investigate two lines of inquiry. The relation ship between height and weight and the relationship between IQ and KS2 math’s results. I will choose a sample of thirty boys and thirty girls randomly. This can be done using a number of methods. I have used the random number button on my calculator.

HEIGHT AND WEIGHT

Below I have shown the sample of the thirty boys and girls that I have chosen.

 Girls Boys Height (m) Weight (kg) Height (m) Weight (kg) 136 44 132 38 142 52 149 67 152 33 150 55 152 55 153 40 154 45 154 42 156 50 154 54 156 53 155 38 156 63 155 43 156 74 155 47 157 45 155 47 157 52 155 64 157 53 155 64 158 40 160 55 158 48 162 48 158 55 162 49 160 42 162 50 160 54 165 46 161 54 165 50 162 42 165 54 162 65 166 43 163 45 166 54 163 48 168 63 165 52 173 50 170 48 174 64 170 50 177 57 172 45 178 67 172 50 180 68 175 53 180 77 175 72 182 75 178 59 183 75

Next I represented this data in the form of a frequency table with boys and girls separately

GIRLS

 Height, h (cm) Frequency Tally 130 ≤ h < 140 1 140 ≤ h < 150 1 150 ≤ h < 160 13 160 ≤ h < 170 8 170 ≤ h < 180 7 180 ≤ h < 190 0

BOYS

 Height, h (cm) Frequency Tally 130 ≤ h < 140 1 140 ≤ h < 150 1 150 ≤ h < 160 10 160 ≤ h < 170 10 170 ≤ h < 180 4 180 ≤ h < 190 4

I next started drawing diagrams show to represent my data. I started analyzing the data using histograms. I used histograms because the data was continuous.

A better comparison of this data can be made using a frequency polygon.

Since the data is grouped into class intervals, I have recorded it in a stem and leaf diagram so to make it easier to find the median.

GIRLS

 Stem Leaf Frequency 130 6, 1 140 2, 1 150 2, 2, 4, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8 13 160 0, 0, 1, 2, 2, 3, 3, 5 8 170 0, 0, 2, 2, 5, 5, 8 7 180 0

BOYS

 Stem Leaf Frequency 130 2, 1 140 9, 1 150 0, 3, 4, 4, 5, 5, 5, 5, 5, 5 10 160 0, 2, 2, 2, 5, 5, 5, 6, 6, 8 10 170 3, 4, 7, 8 4 180 0, 0, 2, 3 4

I also recorded the mean, modal class interval, median and the range so to better compare the data.

 Height (cm) Mean Modal class interval Median Range Girls 160.43 150-160 159 42 Boys 163 150-160-170 162 51

Middle

GIRLS

 Weight, w (kg) Frequency Tally 30 ≤ w < 40 1 40 ≤ w < 50 11 50 ≤ w < 60 14 60 ≤ w < 70 2 70 ≤ w < 80 2

BOYS

 Weight, w (kg) Frequency Tally 30 ≤ w < 40 2 40 ≤ w < 50 9 50 ≤ w < 60 9 60 ≤ w < 70 7 70 ≤ w < 80 3

Then I drew the histograms

To better compare this data I drew a frequency polygon

Since the data is grouped into class intervals, I have recorded it in a stem and leaf diagram so to make it easier to find the median.

GIRLS

 Stem Leaf Frequency 30 3, 1 40 0, 2, 2, 4, 5, 5, 5, 5, 8, 8, 8 11 50 0, 0, 0, 2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 9 14 60 3, 5 2 70 2, 4 2

BOYS

 Stem Leaf Frequency 30 8, 8 2 40 0, 2, 3, 3, 6, 7, 7, 8, 9 9 50 0, 0, 0, 4, 4, 4, 5, 5, 7 9 60 3, 4, 4, 4, 7, 7, 8 7 70 5, 5, 7 3

I also recorded the mean, modal class interval, median and the range so to better compare the data.

 Weight (kg) Mean Modal class interval Median Range Girls 51.37 50-60 51 41 Boys 54.8 40-50-60 54 39

As seen in the table above boys have a greater mean and median yet the modal class interval is higher for the girls. The mean for the boys is higher because there are a greater number of boys with a height greater the 60 then girls, 6 boys more. So the mean is higher. The median is also higher for the boys for the same reasons. So I can conclude by saying that more boys have a greater weight then girls. Also from looking at the data I can say that the weight of the girls is more concentrated between 40kg to 60kg while the weight of the boys is more widely spread out. About 14 out of 30 girls or 46.66% of the girls have a weight between 50kg to 60kg while 9 out of 30 boys or 30% of the boys have a weight between 50kg to 60kg. The same numbers of boys have a weight between 40kg to 50kg.

Conclusion

. It tells us how spread out the data is from the mean.

The method to calculate the standard deviation is as follows:

For each value x, which is the midpoint of the class interval, subtract the overall average x| from x, then multiply that result by itself (otherwise known as determining the square of that value) and then divide it by the frequency f. Sum up all these values. Then divide that result by sum of all the frequencies. Then, find the square root of that last number. Below I have shown the formula for this.

∑ [f(x-x|) 2]

∑f

Now I will calculate the standard deviation of the boys’ height.

 x x-x| (x-x|)2 f f(x-x|)2 135 135-163 = -28 784 1 784 145 145-163 = -18 324 1 324 155 155-163 = -8 64 10 640 165 165-163 = 2 4 10 40 175 175-163 = 12 144 4 576 185 185-163 = 22 484 4 1936 Totals ∑f = 30 ∑f(x-x|)2 = 4300

Standard deviation = √ (4300/30)

Standard deviation for boys’ height = 11.97

Now I will calculate the standard deviation of the girls’ height.

 x x-x| (x-x|)2 f f(x-x|)2 135 135-160.43 = -25.43 646.68 1 646.68 145 145-160.43 = -15.43 238.08 1 238.08 155 155-160.43 = -5.43 29.48 13 383.24 165 165-160.43 = -4.57 20.88 8 167.04 175 175-160.43 = 14.57 212.28 7 1485.96 185 185-160.43=24.57 603.68 0 0 Totals ∑f = 30 ∑f(x-x|)2 = 2921

Standard deviation = √ (2921/30)

Standard deviation for girls’ height = 9.87

The standard deviation for boys is greater then that of the girls by 2.10. So I can say that the values for the boys are more spread out then that of the girls.

Now I will calculate the standard deviation of the boys’ weight.

 x x-x| (x-x|)2 f f(x-x|)2 35 35-54.8 = -19.8 392.04 2 784.08 45 45-54.8 = -9.8 96.04 9 864.36 55 55-54.8 = 0.2 0.04 9 0.36 65 65-54.8 = 10.2 104.04 7 728.28 75 75-54.8 = 20.2 408.04 3 1224.12 Totals ∑f = 30 ∑f(x-x|)2 = 3601.20

Standard deviation = √ (3601.20/30)

Standard deviation for boys’ height = 10.96

Now I will calculate the standard deviation of the girls’ weight.

 x x-x| (x-x|)2 f f(x-x|)2 35 35-51.37 = -16.37 267.98 1 267.98 45 45-51.37 = -6.37 40.58 11 446.35 55 55-51.37 = 3.63 13.18 14 184.48 65 65-51.37 = 13.63 185.78 2 371.55 75 75-51.37 = 23.63 558.38 2 1116.75 Totals ∑f = 30 ∑f(x-x|)2 = 2387.11

Standard deviation = √ (2387.11/30)

Standard deviation for girls’ height = 8.92

The standard deviation for boys is greater then that of the girls by 2.04. So I can say that the values for the boys are more spread out then that of the girls.

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.

## Found what you're looking for?

• Start learning 29% faster today
• 150,000+ documents available
• Just £6.99 a month

Not the one? Search for your essay title...
• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month

# Related GCSE Height and Weight of Pupils and other Mayfield High School investigations essays

1. ## Mayfield. HYPOTHESIS 1: Boys at Mayfield School are Taller and Weigh more on ...

I have collected although this may on some occasion be accurate due to the fact my sample may not be efficient and also the range of data varies where the IQ range for Boys is 21 cm and Girls in 33 cm which shows that the spread of data that

2. ## Conduct an investigation comparing height and weight from pupils in Mayfield School.

= 1.3x + 123 x = y - 123 1.3 So if a person is 175cm tall the equation of the line would suggest If y = 174cm then X = 175 - 123 = 42 = 40 (40 + 25 = 65)

1. ## height and weight investigation

The standard deviation also agrees with that as we can see that the average deviation from the mean is almost 10kg (9.96) and it shows me that the mean doesn't reflect most of the students. The average weight is 50.47 kg and the most common one is 45 kg this

2. ## Boys are taller than girls, I am going to investigate this by looking at ...

1.73 45 10 Long Anne 15 3 April Female 1.74 47 10 Durst Freda 15 4 March Female 1.75 60 10 Dickson Amy 15 9 October Female 1.75 56 Yr 11 boys 11 Francis Henry 16 7 January Male 1.58 54 11 Cripp Justin 16 6 September Male 1.67 50

1. ## Liquid chromatography is a technique used to separate components of a mixture to isolate ...

4.6mm column of Genesis 300� 4� C18 - 100 ? 4.6mm column of Kromasil 5� C18 - 100 ? 10mm column of Genesis 4 � C18 * Samples: - Theophylline - Caffeine - Acetone - Sodium Benzoate * Acetonitrile (HPLC Grade)

2. ## The aim of the statistics coursework is to compare and contrast 2 sets of ...

for year 9 is 161<h<170cm The upper quartile for year 9 is 171<h<180cm The interquartile range for year 9 is - Upper quartile - Lower quartile = 171 - 161 = 20 180 - 160 = 20 The interquartile range = 20<h<20 From the cumulative frequency curve I can say that the median is higher for year 9.

1. ## Maths Data Handling

The line of best fit suggests that a person with a height of 155 cm will be 47 kg, whereas a person of a height of 175 cm will be 56 kg. This shows the difference that height of a person makes towards the weight of that same person.

2. ## The effect of drop jump height on spinal shrinkage.

Thus indicating the drop jump regimen to greater influence shrinkage. At present no investigation has sought to identify, the specific attributes of the drop jump regimen that greatest effect shrinkage. Therefore the study has been necessitated to investigate (1) the shrinkage induced by 2 separate drop jump regimens, and (2)

• Over 160,000 pieces
of student written work
• Annotated by
experienced teachers
• Ideas and feedback to