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  • Level: GCSE
  • Subject: Maths
  • Word count: 4918

For my investigation I will be investigating the statement "Boys are taller than girls."

Extracts from this document...

Introduction

Investigating the statement “Boys are taller than girls.”

Introduction

  For my investigation I will be investigating the statement “Boys are taller than girls.”

Planning

 I will need to collect the year group, gender and height for each person in years 7 and 11 at Mayfield High School. I can find this information from the database the school provided. I have chosen this source of information, as it is reliable. I will use a sample size of total 120 so that is a sample size of about 60 per year group and 30 per year group per gender. This will be a fair sample as it considers a proportional number of people in each year so my results should show a similar variation in each year group therefore giving me better averages to work with. I will use this data to compare the difference in heights between boys and girls in each year group.

Hypothesis  

 My hypothesis is that I think girls will, on average, be taller than boys in year 7 as they start puberty earlier and so grow earlier. In year 11 I think boys will be taller as by this time they have started puberty and have grown taller. From the age of 14 boys generally tend to be taller than girls. So I expect my results to show that boys are taller than girls in the older age groups.

Averages

 There are three main ways of finding an average. These are the; mean, mode and median.

 The mean is the most common way of finding an average. To find the mean there are three easy steps: 1.

...read more.

Middle

1.61

7

Matthews

David

12

Male

1.50

7

McCally

Simon

12

Male

1.45

7

Mills

Robert

John

12

Male

1.63

7

O'Keagan

Kevin

Rourke

12

Male

1.55

7

Partridge

Andy

12

Male

1.74

7

Punnu

Aded

12

Male

1.65

7

Sammy

Singh

Amrit

11

Male

1.52

7

Shaw

Paul

12

Male

1.57

7

Solomon

Christopher

Michael

12

Male

1.56

7

Stanton

Andrew

Lee

12

Male

1.41

I have chosen the following data for my analysis. I have selected my data using stratified sample. Previously I decided to use a sample of 60 pupils per year. I used a stratified sample to get a proportional number of pupils within the year group. The equation I used for the girls gave me the information I needed to be able to tell that I needed to pick twenty-eight out of the sixty pupils. This leaves me with thirty-two pupils once I have subtracted the twenty-eight away from the sixty.

MEAN: I have already completed my first step by collecting all the data. My second step is to add together all the relevant values.

1.62                                            1.64

1.45                                            1.53

1.52                                            1.63

1.36                                            1.54

1.47                                            1.30

1.58                                            1.61

1.60                                            1.50

1.60                                            1.45

1.55                                            1.63

1.71                                             1.55

1.42                                            1.74

1.65                                            1.65

1.50                                            1.52

1.62                                            1.57

1.51                                             1.56

  1. 1.41

=49.60

My second step to finding the mean is to divide the total of the heights by the number of heights.

49.60/32 = 1.55

The mean number of year 7 boys’ heights is 1.55m to the nearest cm.

MEDIAN: My first step to finding the median is to set out the data in numerical order.

1.30                                      1.56

1.36                                      1.57

1.41                                       1.58

1.42                                      1.60

1.45                                      1.60          

1.45                                      1.61

1.47                                      1.61

1.50                                      1.62

1.50                                      1.62

1.51                                       1.63

1.52                                      1.63                                          

1.52                                      1.64  

1.53                                      1.65

1.54                                     1.65                            

1.55                                     1.71      

  1. 1.74

I now must work out the half way point between the numbers. I know there are thirty-two numbers in the sample and so therefore the half way point between the numbers is sixteen and a half. As this is not a whole number I will have to use the mid point between sixteen and seventeen.

Sixteenth number = 1.55

Seventeenth number = 1.56

Mid point number = 1.555

This rounds up to 1.56m    

The median for year 7 boys’ heights is 1.56m.

MODE: To work out the mode I need to work out how many of each height there are in this sub set. To do this I will set out the data with the number of that height next to it in brackets.

1.30 (1)                                      

1.56 (1)

1.36 (1)                                    

 1.57 (1)

1.41 (1)                                  

   1.58 (1)

1.42 (1)                                    

1.60 (2)

1.45 (2)                                              

1.61(2)

1.47 (1)                                      

1.62(2)

1.50 (2)                                    

1.63(2)

1.51 (1)                                    

1.64(1)

1.52 (2)                                    

1.65(2)

1.53 (1)                                  

1.71(1)

1.54 (1)                                                  

1.74(1)

1.55 (2)                                    

From the presentation of this data I can see that there is more than one mode they are 1.45m, 1.50m, 1.52m, 1.55m, 1.60m, 1.61m, 1.62m, 1.63m and 1.65m as they are the heights with the most people from the sample.

The modal values for year 7 boys’ heights are 1.45m, 1.50m, 1.52m, 1.55m, 1.60m, 1.61m, 1.62m, 1.63m and 1.65m.

 A box plot diagram and histogram will help show the ranges and present data.

Standard deviation is a good measure of spread as it tells how far away each value in the data is away from the mean.

X

X – X

(X - X)

1.3

0.25

0.0625

1.36

0.19

0.0361

1.41

0.14

0.0196

1.42

0.13

0.0169

1.45

0.1

0.01

1.45

0.1

0.01

1.47

0.08

0.0064

1.5

0.05

0.0025

1.5

0.05

0.0025

1.51

0.04

0.0016

1.52

0.03

0.0009

1.52

0.03

0.0009

X=49.6/32 = 1.55

1.53

0.02

0.0004

S= 0.2964/32 =0.017 to 4 sf

1.54

0.01

0.0001

1.55

0

0

1.55

0

0

1.56

-0.01

0.0001

1.57

-0.02

0.0004

1.58

-0.03

0.0009

1.6

-0.05

0.0025

1.6

-0.05

0.0025

1.61

-0.06

0.0036

1.61

-0.06

0.0036

1.62

-0.07

0.0049

1.62

-0.07

0.0049

1.63

-0.08

0.0064

1.63

-0.08

0.0064

1.64

-0.09

0.0081

1.65

-0.1

0.01

1.65

-0.1

0.01

1.71

-0.16

0.0256

1.74

-0.19

0.0361

Total

49.6

0.00

0.2964

The standard deviation of year 7 boys’ heights is 0.017 to four significant figures.

Analysing Boys and Girls Heights in Year 7

 From the data shown above I can see that, on average, boys and girls are very similar heights although girls have a slightly taller average height. We can also see that girls have a larger range of heights than boys through the box plot diagrams and the standard deviation results. In my hypothesis I thought that girls would be taller than boys in year 7, therefore my hypothesis correct, although I did believe that the difference between girls heights and boys heights would be much greater.

SUB SET – year 11 girls

Year Group

Surname

Forename 1

Forename 2

Years

Gender

Height (m)

11

Acton

Jenny

Sarah

16

Female

1.67

11

Ali

Amera

15

Female

1.62

11

Barlow

Louise

Jane

16

Female

1.63

11

Becher

Heidi

Francis

16

Female

1.72

11

Berry

Shelly

Laura

16

Female

1.73

11

Bertwistle

Lara

Alyson

16

Female

1.63

11

Bradbury

Natalie

Angela

16

Female

1.69

11

Brown

Amy

Ruth

16

Female

1.62

11

Brown Isabella

15

Female

1.65

11

Buyram

Dawn

Elizabeth

16

Female

1.65

11

Chen

Sabrina

16

Female

1.61

11

Compass

Sharon

Stella

16

Female

1.52

11

Dion

Dawn

Stella

16

Female

1.68

11

Dorn

Shelly

Michelle

16

Female

1.63

11

Feehily

Christina

Jean

16

Female

1.72

11

Flawn

Elise

16

Female

1.62

11

Grace

Davina

16

Female

1.65

11

Grot

June

Leah

16

Female

1.60

11

Hall Julie

16

Female

1.63

11

Heap

Louise

Stephanie

16

Female

1.80

11

Hunter

Ingrid

16

Female

1.52

11

Jackson

Debi

16

Female

1.68

11

Kaleem

Humaira

16

Female

1.69

11

Kay

Nadia

16

Female

1.62

11

Kelly

Sarah

16

Female

1.55

11

Khan

Adila

16

Female

1.63

11

Margeus

Nichola

Paula

16

Female

1.61

11

McCarthy

Farrah

16

Female

1.59

11

McCreadie

Jenny

16

Female

1.62

11

McMillan

Collen

Jade

16

Female

1.58

...read more.

Conclusion

1.52  (1)                                  

1.75  (1)  

1.55  (1)                                 

1.77  (1)

1.58  (1)                                 

1.78  (1)

1.62  (4)                                 

1.8   (1)

1.67  (3)                                  

1.82  (1)

1.68  (4)                                    

1.85  (1)  

1.69  (1)

1.86  (2)   

1.7   (1)

1.92  (1)

1.71  (1)

1.94  (1)

1.72  (2)

1.96  (1)

From the presentation of this data I can see that the modal values are 1.62m and 1.68m as they are the heights with the most people from the sample.

  The modal values for year 11 boys’ heights are 1.62m and 1.68m.

A box plot diagram and histogram will help show the ranges and present data.

Standard deviation is a good measure of spread as it tells how far away each value in the data is away from the mean.

X

X - X

(X - X)

1.52

0.203666667

0.04148

1.55

0.173666667

0.03016

1.58

0.143666667

0.02064

1.62

0.103666667

0.010747

1.62

0.103666667

0.010747

1.62

0.103666667

0.010747

1.62

0.103666667

0.010747

1.67

0.053666667

0.00288

1.67

0.053666667

0.00288

1.67

0.053666667

0.00288

1.68

0.043666667

0.001907

X= 51.71/30 = 1.72 to 2 dp

1.68

0.043666667

0.001907

S= 0.368897/30 = 0.020 to 4 sf

1.68

0.043666667

0.001907

1.68

0.043666667

0.001907

1.69

0.033666667

0.001133

1.7

0.023666667

0.00056

1.71

0.013666667

0.000187

1.72

0.003666667

1.34E-05

1.72

0.003666667

1.34E-05

1.75

-0.026333333

0.000693

1.77

-0.046333333

0.002147

1.78

-0.056333333

0.003173

1.8

-0.076333333

0.005827

1.82

-0.096333333

0.00928

1.85

-0.126333333

0.01596

1.86

-0.136333333

0.018587

1.86

-0.136333333

0.018587

1.92

-0.196333333

0.038547

1.94

-0.216333333

0.0468

1.96

-0.236333333

0.055853

Total

51.71

0.00

0.368897

The standard deviation of year 11 boys’ heights is 0.020 to four significant figures.

Analysing Boys and Girls Heights in Year 11

 From the data shown above I can see that boys are taller than girls in year 11. We can also see that boys have a larger range of heights than girls through the box plot diagrams and the standard deviation results. The reason for this is that boys generally grow more than girls and so there will be more fluctuation in boys’ heights than girls’ height leading to the greater range. In my hypothesis I thought that boys would be taller than girls in year 11, therefore my hypothesis is correct at this stage.

Conclusion

 Overall I got my hypothesis correct. I predicted that girls would be taller than boys in year 7 and boys to be taller than girls in year 11. My results reflected this prediction well. Generally all my averages worked out well although some better than others. My measures of spread proved helpful when analysing the data.  

Andrew Greaves 10S

...read more.

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