- Level: International Baccalaureate
- Subject: Maths
- Word count: 2394
Interdisciplinary Unit
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Introduction
Interdisciplinary Unit
In
Mathematics and Physical Education
INTRODUCTION
My Project is directed on two different subjects – Mathematics and Physical Education. That is why my project has a lot of aims, which are connected not to only one science. My mathematical aims are to collect and display data using a variety of representations, to interpret and analyze the findings using statistics, to determine the physical fitness of the class using statistics and to compare your fitness level with the mean values for the class and analyze my overall fitness. There are also aims connected to Physical Education, I will tell about them in the second report for Physical Education. I think this project is linked with one Area of Interaction is Health and Social Education, because during the project we did sport exercises, we knew ours sport abilities and overall sport abilities of typical 10 grade's student, we thought about sport program for ourselves and for others to improve our sport skill and health.
INVESTIGATION
How did I get the data?
On the PE lesson my class and me collected some data about our physical abilities. The data were – pulse, endurance, speed, push-ups, sit-ups and flexibility. For measuring the pulse we with special medical tool, and for endurance our trainer counted how long we are running 400 km, for speed we ran 30 meters and our trainer counted how many second did it take.
Middle
7,6
9,9
range
41,0
1,54
1,42
39
21
31
32
37
Central tendencies
Then I calculated and displayed the mean, median, mode, range and standard deviation for each set of class data.
MEAN is one of the more common statistics. And it's easy to compute. All you have to do is add up all the values in a set of data and then divide that sum by the number of values in the dataset. For example:
Sam did 40 sit – ups, Mary 29 sit-ups and Eddy 30 sit-ups, so mean is (40+29+30)/3=33.
MEDIAN is statistic that tells you something about something in the middle.
Again, this statistic is easy to determine because the median literally is the value in the middle. Just line up the values in your set of data, from largest to smallest. The one in the dead-center is your median.
MODE is statistic of central tendency that show the most frequent meaning.
The standard deviation (STDEV) is a statistic that tells you how tightly all the various examples are clustered around the mean in a set of data. When the examples are pretty tightly bunched together and the bell-shaped curve is steep, the standard deviation is small. When the examples are spread apart and the bell curve is relatively flat, that tells you you have a relatively large standard deviation.
It is calculated by the formula: STDEV= √ ([(x1-mean)+(x2-mean)+(x3-mean)]/n)
RANGE is the simplest possible measure of spread and is the difference between the upper extreme value and the lower extreme value.
Best representation of data
I found all central statistics of all data, and concluded that:
- I think that for PULSE measure of central tendency that represent it is mean or median ( they are nearly the same), because mode shows 80 which is 3 student's result, but there is 90 which result of 3 students as well, and mean and median shows 87,2 and 88 – results which is between 80 and 90, other central tendencies gave very low result.
- To know the central tendency of SPEED is better to use mean, median and mode, because here they are nearly the same, so it does not matter, also other central tendencies is too low.
- The central tendency of PUSH-UPS best of all represented by mean and median (they have absolutely the same results – 36,5), mode is bad because it gave too many results, STDEV gave very low result, and range gave close, but not very much result.
- Mean, median and mode are best in measuring central tendency of SIT-UPS, STDEV and range didn't give suitable result.
- To know the central tendency of FLEXIBILITY mean or median because mode gives 2 results, STDEV and range gave unsuitable results again.
- The central tendency of HEIGHT best of all represented by mode, mean and median (they are nearly the same) other central tendency is too low.
- In my opinion mean is best in measuring central tendency of WEIGHT because mode and median a little bit smaller, but this difference is plays a big role (5 kg), range and STDEV gave low results as usual.
- For ENDURANCE the best central tendency I think is mean, because endurance meanings is very different so made can be not exist, also because it is very different mean is most correct, median shows not very good result.
Making of table of frequency and histogram
I've made a frequency table for each data, where is presented how many people have results in one period. For example how many students have results of sit-ups between 31 and 35 - there is10 students.
Here are frequency tables of data I've collected.
Bin | Frequency | Bin | Frequency | Bin | Frequency | |||
5 | 1 | |||||||
20 | 1 | 30 | 4 | 10 | 0 | |||
25 | 4 | 35 | 10 | 15 | 5 | |||
30 | 4 | 40 | 5 | 20 | 6 | |||
35 | 2 | 45 | 1 | 25 | 3 | |||
40 | 1 | 50 | 1 | 30 | 5 | |||
45 | 3 | More | 0 | 35 | 1 | |||
50 | 3 | Sit up | More | 0 | ||||
55 | 2 | Flexibility | ||||||
More | 1 | |||||||
push up | ||||||||
Bin | Frequency | Bin | Frequency | Bin | Frequency | |||
155 | 2 | 50 | 4 | 65 | 1 | |||
160 | 0 | 55 | 4 | 70 | 1 | |||
165 | 4 | 60 | 5 | 75 | 1 | |||
170 | 6 | 65 | 4 | 80 | 3 | |||
175 | 7 | 70 | 2 | 85 | 2 | |||
180 | 0 | 75 | 0 | 90 | 6 | |||
185 | 1 | 80 | 1 | 95 | 2 | |||
More | 1 | 85 | 1 | 100 | 3 | |||
height | More | 0 | 105 | 2 | ||||
Weight | More | 0 | ||||||
pulse |
Conclusion
Also during the project I've learnt to use Microsoft Excel. I didn't use it before and I'm glad that now I know how to use it, because this program can be necessary in my future profession.
During the work there were some problems. First problem is that data can be inaccurate, because for example may be one of the student couldn't do exercises well because of stomachache or other reasons ( illness, uncomfortable trainers, etc), also measuring can be incorrect, because we didn't check them. I think that we needed to check them to make data more correct also student should be sure that nothing prevent them to do exercises. Also while working on Microsoft Excel it is problematic to use mode, because, for example, if there are 10, 12, 12, 12, 15, 20, 20, 20, mode shows only 12 because it is first, but there is 20 is also 3 times. So I needed to check the column and add other meanings. Also there was my personal problem – I don't have Microsoft Excel on my PC. So I needed to work with Excel only at school.
It is really very helpfully that we use the computer to calculate some statistics or to draw graphs. Because if we did do it ourselves it would take too many time and results would be incorrect and inaccurate. Although I have done some calculations, graphs, tables by hand.
MIRAS International School
Interdisciplinary Unit
In
Mathematics and Physical Education
Sanym Paritova
Grade 10
Astana 2007
This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.
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