- Level: AS and A Level
- Subject: Maths
- Word count: 2535
I believe that boys in year 10 are better at estimating time than girls are.
Extracts from this document...
Introduction
Maths Statistical Coursework
For this piece of coursework I am going to analyse some data from a guesstimate survey that was carried out at school. It was asked to students in years 8 and 10. The survey was organised into several categories. These were:
- Girl And Boy
- Year 8 and Year 10
Each student was given the questionnaire, which tested their accuracy in guessing lengths, weights and times.
I myself did not collect the data from the students so it is classed as secondary data. I shall go through all of the results to check for bias results so that I can get the most accurate result. If I end up with bias results I could end up with inaccurate results.
Before observing the data I will make 2 clear hypothesis’s.
Hypothesis 1
I believe that boys in year 10 are better at estimating time than girls are. To start off I shall start of by using the 60 seconds question to attempt to prove or disprove it. My hypotenuse might expand the more I get into my results.
Proving
To prove this I shall take a sample of the data taken in by this questionnaire. Form this I shall
Middle
10
65
F
10
59
F
10
62
F
10
62
F
10
60
F
10
60
F
10
60
Before I work out some results I shall search through my data to search for anomalies. Whilst searching through my results I have found out that there aren’t any results that seam biased. As it was a guess of time I believe it depends on the person and there knowledge of how long a second is when they don’t have a clock to check when a minuet is up.
Useful calculated results for the mean, median, mode and range would be useful in the analysis of my results.
Mean - 57.9
Median – 60
Mode – 60
Range – 47
Cumulative Frequency Diagram
To prove that the mean time guess for 60 seconds from the girls was 57.9 I shall draw up a cumulative frequency diagram to show the median, and the inter quartile range.
Time (s) | Frequency | Cumulative Frequency |
25 < h < 30 | 1 | 1 |
30 < h < 35 | 0 | 1 + 0 = 1 |
35 < h < 40 | 1 | 1 + 1 = 2 |
40 < h < 45 | 1 | 2 + 1 = 3 |
45 < h < 50 | 3 | 3 + 3 = 6 |
50 < h < 55 | 8 | 6 + 8 = 14 |
55 < h < 60 | 17 | 14 + 17 = 31 |
60 < h < 65 | 14 | 31 + 14 = 45 |
65 < h < 70 | 3 | 45 + 3 = 48 |
70 < h < 75 | 0 | 48 + 0 = 48 |
75 < h < 80 | 1 | 48 + 1 = 49 |
The Useful thing about a cumulative frequency graph is that it gives you more detailed information about the set of data. In particular it is used to find the median and the inter-quartile range. The inter-quartile range describes how spread out the results are given are.
Insert Graph 2
This graph above tells me that the median is 58 seconds and that the inter- quartile range is the upper quartile minus the lower quartile. This means that the Inter-quartile range = 62 – 54 = 8. So the inter quartile range is 8.
Using A Histogram
For use in my statistical graphs and diagrams I shall group my data into groups to make analysis.
I shall end up using unevenly groped data, as I will find that some groups will contain a substantially larger amount of data that would fit into that category. So using this method means that I will get some evenly spread data, which will make it more accurate to analyse as I will have a better spread of the results.
20 - 30 | 31 - 40 | 41 - 50 | 51 - 55 | 56 - 58 | 59 - 60 | 61 - 64 | 65 - 80 |
1 | 1 | 4 | 8 | 6 | 10 | 12 | 6 |
Conclusion
A good way of comparing the two’s results is by putting your results into a box and whisker diagram. This diagram shows me some crucial bits of results all in one easy to analyse diagram. Lets compare the two.
As you can see from these box and whisker diagrams the diagrams show you all of the answers that you could need in on place. All you have to know is where to look. I have written on the box and whisker diagrams exactly what part of the diagram shows you what piece of evidence.
Conclusion
In conclusion I have noticed that the boys are better at estimating when a period of time (60 seconds) has past mentally. I believe that the strategy that I used to make up this result was a very good way to go about what I had been asked to do. I believe that I had increased/decreased the sample size then the results might of changed. But since I was only taking the size of around 50 I could have accidentally picked all of the boys best results, or even all of the girls best results. The way that you have to put limitations on this piece of coursework has confined the results into a rather small selection. If I had picked something that was larger, who knows what could have happened.
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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