# Reaction Times

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Introduction

Maths Statistics Coursework: Reaction times

Reaction Times

Plan

Hypotheses: 1) Boys are faster than girls are

2) Right-handed students are faster than left-handed students are

3) Right-handed boys are faster than right-handed girls are

Possible methods of testing

- Hit the mole (arcade game)- I would time how many moles they could hit in one minute, repeat this 3 times to get a fair result and then find an average. This would be read as the higher the number of moles that are hit, the faster the reaction. However you would have to travel to an arcade to carry this test out and it would be extremely expensive.

- Stopwatch- I would tell the student to stop it at a certain time e.g. 2 minutes, and however many seconds before or after they stopped the stopwatch, would be their reaction time, the closer the number of seconds it is to 2 minutes, the faster the reaction. This would of course be repeated 3 times to get a fair result and then the average found. However the stopwatch buttons may get stuck, therefore altering results.

- Dropping a ruler- I would take a 30cm ruler and make sure that the zero is inline with the index finger.

Middle

Tally

Frequency

Frequency density

0 < r < 5

0

0/5=0

5 < r < 10

0

0/5=0

10 < r < 20

12

12/10=1.2

20 < r < 25

0

0/5=0

25 < r < 30

0

0/5=0

I will use a Histogram, to find the median. As I expect the right-handed students to be faster, I will expect the median for the right-handed students to be lower than for the left-handed students.

Right-handed Median = 13.5

Left-handed Median = 15

Conclusion for Hypothesis 2

The medians again prove that my 2nd hypothesis is correct. Right-handed students are faster than left-handed students because the right-handed students achieved a median of 13.5 whereas the left-handed students achieved a median of 15, making the right-handed students’ average faster.

Testing

Hypothesis 3

Right-handed boys are faster than right-handed girls are

I found the averages for my sample of 50 students, and decided to arrange the results into grouped-data tables for convenience and accuracy. My groups were decided as: -

Reaction (cm’s)

0-5 extremely fast

5-10 fairly fast

10-20 average

20-25 slow

- very slow

The results for right-handed boys were as follows-

Reaction | Tally | Frequency | Mid-point | Mid-point x Frequency | |

0 < r < 5 | 0 | 2.5 | 0 x 2.5=0 | ||

5 < r < 10 | 10 | 7.5 | 10 x 7.5=75 | ||

10 < r < 20 | 15 | 15 | 15 x 15=225 | ||

20 < r < 25 | 02 | 22.5 | 2 x 22.5=45 | ||

25 < r < 30 | 0 | 27.5 | 0 x 27.5=0 | ||

27 | 345 |

The results for right-handed girls were as follows-

Reaction | Tally | Frequency | Mid-point | Mid-point x Frequency | |

0 < r < 5 | 0 | 2.5 | 0 x 2.5=0 | ||

5 < r < 10 | 7 | 7.5 | 7 x 7.5=52.5 | ||

10 < r < 20 | 13 | 15 | 13 x 15=195 | ||

Conclusion

I found the standard deviations for the right-handed girls and boys. It showed that the boys were more consistent than the girls were.

Conclusion for Hypothesis 1

The Median for the boys is 10 whereas the median for the girls is 13. This already proves my hypothesis correct boys are faster than girls are.

Also, on the box-plots ¾ of the boys have a reaction between 10 and 13 whereas ¾ of the girls have a reaction between 13 and 17, so the majority of boys are faster than the girls are.

I can also see from the whiskers of the box plots that there are outliers. There is a boy who is extremely slow in comparison to the majority of the boys and a girl who is also extremely slow in comparison to the majority of the girls.

The steepness of the boys’ graph proves again that the boys have a faster reaction than the girls do.

Furthermore, I can see from the inter-quartile ranges, (which represent the middle-half of the sample) that the girls are slower, the reaction of the middle half being 6.5 and the boys’ being 4.5.

In addition to this, I can see from the inter-quartile ranges that the boys are more consistent as their range is closer together 8.5 – 13 compared to the girls ranging from 10.5 - 17

Kiran Virdee 10SNA Page 5/10/2007

This student written piece of work is one of many that can be found in our AS and A Level Probability & Statistics section.

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