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• Level: GCSE
• Subject: Maths
• Word count: 2740

Show that different people have different reaction times according to their gender and the size of their hand span.

Extracts from this document...

Introduction

Mathematics GCSE Coursework

Reaction Times

Introduction:

I am going to show that different people have different reaction times according to their gender and the size of their hand span. I will try to prove this by selecting a number of people, and testing their reaction times. I will record their reaction times in a table and then analyze them to produce a set of reliable results.

Hypothesis:

My first hypothesis is that people with a smaller hand span have quicker reaction times.

My second hypothesis is that males have quicker reaction times than females.

Method:

For this experiment I am going to use primary data. This means that I will collect the data myself as I am the one going to use it.

The way in which I will record the reaction times of the people I select will be to use a 10cm ruler.

I will ask the person to hold out their hand as if they were holding a burger, with their fore finger and thumb 2cm apart. I will then hold the ruler upright (0cm at the bottom, 10cm at the top) above their hand so the bottom edge is level with their fore finger and thumb.

Middle

15.0

17.0

24.11.87

20.0

Female 03

12.0

24.0

14.0

16.7

01.03.88

20.0

Female 04

22.0

17.0

18.0

19.0

03.07.88

17.0

Female 05

21.0

22.0

23.0

22.0

26.08.88

19.5

Female 06

26.0

23.0

26.0

25.0

16.05.88

19.5

Female 07

14.0

22.0

26.0

20.7

21.04.88

18.0

Female 08

17.0

12.0

17.5

15.5

19.10.87

15.0

Female 09

10.5

13.5

04.5

09.5

04.07.88

15.0

Female 10

08.0

17.0

06.0

10.3

04.05.88

18.5

Female 11

14.5

09.0

10.0

11.2

29.11.87

18.5

Female 12

12.5

13.5

17.5

14.5

17.05.88

19.0

Female 13

20.0

21.0

14.0

18.3

07.03.88

16.5

Female 14

27.0

14.0

21.0

20.7

08.06.88

17.0

Female 15

13.0

13.0

14.0

13.3

28.09.87

19.0

Female 16

26.0

18.0

17.5

20.5

14.03.88

18.0

Female 17

19.0

15.5

20.0

18.2

21.10.87

18.5

Female 18

17.0

18.0

14.0

16.3

05.12.87

19.0

Female 19

16.5

16.0

11.5

14.7

17.02.88

20.0

Female 20

09.0

13.0

14.0

12.0

26.12.87

20.0

Female 21

23.0

11.0

13.0

15.7

26.07.88

20.0

Female 22

18.0

13.5

05.0

12.2

04.02.88

18.0

Female 23

08.0

15.0

11.0

11.3

22.03.88

17.0

Female 24

14.0

15.0

21.0

16.7

10.07.88

16.0

Males:

 Reaction Time Frequency Cumulative Frequency 0 > 5 0 0 5 > 10 1 1 10 > 15 9 10 15 > 20 13 23 20 > 25 1 24 25 - 30 0 24

Females:

 Reaction Time Frequency Cumulative Frequency 0 > 5 0 0 5 > 10 1 1 10 > 15 8 9 15 > 20 10 19 20 > 25 4 23 25 - 30 1 24

Cumulative Frequency:

This graph shows that the fastest females are just as fast as the fastest males, however, as the reaction times get slower, the slowest female has a slower reaction time than the slowest male. Females have a bigger range.

This graph does not seem to be accurate enough to obtain the lower quartile, the median and the upper quartile from. So instead of reading the graph to obtain these values, I worked them out by putting all the average reaction times in order.

Box and whisker diagrams:

A good way of showing overall results is to use box and whisker diagrams:

This shows that overall males have a slightly faster reaction time than females. This proves my hypothesis is right. However, there could be a large margin for experimental error. This margin would be severely reduced if more measurements were taken.

Scatter diagrams:

A scatter diagram is a good way of seeing if thee is any correlation in your data.

Conclusion

"c0">4.0

16.00

Male 07

17.7

21.0

15.5

19.5

-4.0

16.00

Male 08

14.7

22.0

20.5

10.0

10.5

110.25

Male 09

15.7

21.0

15.5

14.0

1.5

2.25

Male 10

15.2

20.0

09.0

11.5

-2.5

6.25

Male 11

12.7

09.5

01.0

05.0

-4.0

16.00

Male 12

17.3

22.0

20.5

18.0

2.5

6.25

Male 13

17.0

20.0

09.0

17.0

-8.0

64.00

Male 14

24.3

17.0

02.5

24.0

-21.5

462.25

Male 15

14.0

21.0

15.5

08.0

7.5

56.25

Male 16

19.0

21.0

15.5

22.0

-6.5

42.25

Male 17

15.2

17.0

02.5

11.5

-9.0

81.00

Male 18

05.7

19.0

06.5

01.0

5.5

30.25

Male 19

11.3

21.0

15.5

03.5

12.0

144.00

Male 20

19.5

20.0

09.0

23.0

-14.0

196.00

Male 21

17.7

23.0

22.5

19.5

3.0

9.00

Male 22

13.0

19.0

06.5

06.0

0.5

0.25

Male 23

10.7

21.0

15.5

02.0

13.5

182.25

Male 24

16.0

23.0

22.5

15.5

7.0

49.00

∑d2

1681.50

Spearmans Rank

0.27

From the table the Spearmans coefficient of rank correlation is 0.27 for the males. This shows a weak positive correlation of hand span to reaction time.

 Average (cm) Hand span (cm) Hand span Rank Average rank d d x d Female 01 16 20 21.5 12.0 9.5 90.25 Female 02 17 20 21.5 16.0 5.5 30.25 Female 03 16.7 20 21.5 14.5 7.0 49.00 Female 04 19 17 6.0 19.0 -13.0 169.00 Female 05 22 19.5 17.5 23.0 -5.5 30.25 Female 06 25 19.5 17.5 24.0 -6.5 42.25 Female 07 20.7 18 9.0 21.5 -12.5 156.25 Female 08 15.5 15 1.5 10.0 -8.5 72.25 Female 09 9.5 15 1.5 1.0 0.5 0.25 Female 10 10.3 18.5 12.0 2.0 10.0 100.00 Female 11 11.2 18.5 12.0 3.0 9.0 81.00 Female 12 14.5 19 15.0 8.0 7.0 49.00 Female 13 18.3 16.5 4.0 18.0 -14.0 196.00 Female 14 20.7 17 6.0 21.5 -15.5 240.25 Female 15 13.3 19 15.0 7.0 8.0 64.00 Female 16 20.5 18 9.0 20.0 -11.0 121.00 Female 17 18.2 18.5 12.0 17.0 -5.0 25.00 Female 18 16.3 19 15.0 13.0 2.0 4.00 Female 19 14.7 20 21.5 9.0 12.5 156.25 Female 20 12 20 21.5 5.0 16.5 272.25 Female 21 15.7 20 21.5 11.0 10.5 110.25 Female 22 12.2 18 9.0 6.0 3.0 9.00 Female 23 11.3 17 6.0 4.0 2.0 4.00 Female 24 16.7 16 3.0 14.5 -11.5 132.25 ∑d2 2204.00 Spearmans Rank 0.04

From the table the Spearmans coefficient of rank correlation is 0.04 for the females. This shows no correlation as it is so close to 0.

Conclusion:

From the box and whisker diagrams, the cumulative frequency diagrams and the histograms there is evidence to show that my hypothesis “males have faster reaction times to females” could be correct.

From the scatter diagrams and Spearmans coefficient of rank correlation I have concluded that there is little correlation between the size of a persons hand span and their reaction time. The correlation is so low that my hypothesis “the smaller a persons hand span the quicker their reaction time” is probably incorrect.

Simon Beard 10Y

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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