Eg. 124/1014*100 = 12.2287… = 12
For this experiment, I will be taking a sample of 100 people. To do this from the 1014 people in our school, I divided up each year group into males and females, then took a proportional population.
Raw Data
Both the sets of data were collected in millimetres, which is the length the person caught it at in accordance to the ruler.
By using the ‘law of motion’ I can determine the amount of time the ruler fell for before it was caught. We can call this the reaction time. By using this formula I can work the reaction time out.
s=ut+½at²
u = initial velocity s = distance a = acceleration t = time
(9.81 metres)
In this particular case, u = 0 as the ruler is always stationery to begin with. Due to this factor, this makes “u” useless, and the formula can be rearranged into:
s=½at²
As ½a multiplied by t² is equivalent to s, so 2s must be equivalent to at².
2s=at²
As ‘a’ is multiplied by t² to form 2s so t² must equal 2s/a.
This can be rearranged to form:
√2s/a=t
In order for excel to understand this formula, we change it to this:
√2s/a=t
=SQRT ((……………/100)*2)9.81
We had to divide by 100 so that the reaction time was in seconds. If we had not done this, it would have made the results appear to be in minutes; therefore making the reaction time for someone catching a ruler a lot longer than it actually took the person.
Then using the formulae to work out the reaction time:
The standard deviation is a way of comparing 2 sets of data.
√∑(x-x)²
n
x – piece of data
x – mean of the set of data
n – number of pieces of data
∑ - ‘sum of’
Using this data I can begin to start working on the hypotheses. Firstly, I will create a scatter graph and work out the correlation coefficient to see if there is a link between the two sets of time data.
Hypothesis 1
Correlation
From this it is possible to see a weak positive correlation between the two sets of results. Looking at the correlation coefficient (a number between –1 and 1) which shows between 2 sets of data the size of the correlation: -
The correlation co-efficient is: 0.548655.
Normally for a good link to exist this number should be above 0.7 so we can see that there is not a great relationship between the two sets but that there is at least a small connection.
First of all I sorted the data. Then I drew up 2 cumulative frequency tables.
From these I then constructed a cumulative frequency graph.
From the cumulative frequency diagram I can see that the non-distraction times are quicker as the have more of a steep curve. The times with Distraction have not got as steep a curve, which shows that the reaction times are not as fast as those which haven’t been distracted.
The mean, the median and the mode of the non-distraction times are lower than the distraction times. This shows that the non-distraction times are faster than the times with a distraction, this helping prove my hypothesis. The minimum values of non-distraction times are 0.04, and the minimum value of distraction times is 0.13. This shows that the lowest time of non-distraction is lower than the distraction time, proving that reaction times are quicker without a distraction.
By comparing the mean of both sets of data I can tell determine that the result which is lowest, meaning it has the best time of reaction, is the one with no distraction. Next, I have compared the standard deviation, which is a method of comparing the spread of two sets of data again, the lower of the two is the one which indicates which is the better reaction time. In this case, the quicker reaction time is without a distraction.
Hypothesis 2
For this hypothesis, I predicted that the difference between the two sets of results would be lower for the females, and higher for the males.
I started by creating an extra column in Excel, and using Excel to work out the difference between the two columns, and sorting the data into male and female.
I then worked out the mean, median, minimum, maximum, and the range of the differences on Excel.
Next, I worked out the standard deviation of the differences on Excel.
Female: 0.0581
Male: 0.0494
Standard Deviation is a method of comparing the spread of two sets of data.
The mean of the differences for the females is lower, than for the males. This makes the females better at multi-tasking as the closer to 0 the difference is, the more consistent the times are, which means the candidate has a consistent reaction time, thus meaning they are more consistent. The maximum for the males is lower than the maximum for the females. This shows that the males results are more tightly grouped and are not as all over the place as the females.
I then made up these tables, so I could then construct a Histogram from them.
Females
Males
From the Histogram I can tell that the majority of the males’ differences are between 0.04 and 0.1, whereas the females’ results are spread a little more evenly, although the majority is also between these boundaries. In every other boundary, the females have a higher frequency density, showing that the majority of males’ differences are banded within the fore mentioned boundary.
I then made a Frequency Polygon, 1 for the male results, 1 for the female results.
The Frequency Polygons show that the male spread is within the middle towards the end. The female
spread is fairly consistent, though they have higher results, and the majority results are at the beginning.
I have found out that females are better at multi tasking than males. This is true because the mean for the females is lower than the males; the median is lower for the females. This shows that the results are more consistent, therefore making them better at multi tasking than men.
The frequency polygon shows that the female spread is more consistent than the males, as the males has a fluctuation in the middle, whereas the female results are fairly consistent throughout.
From the histogram I can tell that the females’ differences are spread more evenly than the males, as the males’ differences are concentrated in the middle area.
These factors prove that females are better at multi tasking than males.
The Overall Conclusion.
My first hypothesis was that I thought Reaction times would be faster without a distraction. I have used a cumulative frequency graph, a scatter graph, the mean, median, mode, the minimum and maximum results, standard deviation and correlation co-efficient to successfully prove my hypothesis correct.
My second hypothesis was that I thought that the difference between the two sets of results, being distracted or not, will be lower for the girls and higher for the boys. I used the mean, median, mode, minimum and maximum results, a Histogram and Frequency Polygons to successfully prove that females are better at multi tasking.
