- Level: International Baccalaureate
- Subject: Maths
- Essay length: 2556 words
Math Portfolio Type I
Extracts from this essay...
Introduction
Type 1 The procedure to carry on this portfolio was followed according to the given instructions which are mentioned in the attached sheet. DATA ANALYSIS The following table was made by taking the weight of 100 students of classes 10th and 12th from the school's dispensary. (With the use a Microsoft Excel Sheet) Weights Number of Students 34 35 1 36 37 38 39 40 2 41 1 42 2 43 1 44 2 45 4 46 1 47 3 48 49 2 50 7 51 52 53 2 54 6 55 5 56 4 57 3 58 2 59 3 60 3 61 2 62 6 63 64 5 65 6 66 1 67 1 68 2 69 70 3 71 1 72 1 73 3 74 75 1 76 1 77 1 78 2 79 1 80 1 81 1 82 83 84 2 85 86 87 88 89 90 3 91 92 93 94 95 1 96 97 98 1 99 100 This table was further processed by making a table (shown bellow) containing weights (xi), number of students having the respective weight (fi) and the product of both (with the help of Microsoft Excel) of them (fixi). Weights (xi) Number of Students (fi) xi fi 34 0 35 1 35 36 0 37 0 38 0 39 0 40 2 80 41 1 41 42 2 84 43 1 43 44 2 88 45 4 180 46 1 46 47 3 141 48 0 49
Middle
After obtaining the two graphs of different class intervals (i.e. 10 & 5) while We can compare the shape of the curves, the standard deviation and the mean between them. The two curves are not symmetrical due to various reasons: The curve with class interval of 10 has a small fall at the interval of 80 - 90 this is because of the very less amount of people with this weight. The same thing occurs in the second graph for the class interval of 5 at the interval of 85 - 90. This is the reason why the curves have a non - asymmetrical shape. The two graphs can also be compared in terms of mean the red curve which is of the class with of 5 shows us a closer (which is the actual one) than the blue line that is of a class interval of 10. The two graphs can also be compared by the standard deviation as we can see that the data is more compressed in the curve made by the standard deviation of 10 the data is more compressed than the curve made with the class interval of 5 which hence, shows us that greater the class interval, smaller the dispersion of data and smaller the class interval greater is the scattering of data. To prove all these above mentioned points a random sample of 40 weights was taken (with the class width of 10 and 15).
Conclusion
This positive skewness is because; the mean is greater than the mode or the median. This is also positive skewness since, the large tail of the distribution lies toward the higher values of the variable (i.e. right). 6. What will be the relationship between any population mean and the mean of a sampling distribution taken from it? The main difference between a population mean and a mean of a sample of the population is the standard deviation (i.e. the scattering of data), the mean itself and the mode. This is again because of, the class width taken for each sample of the population. 7. What will be the relationship between their shapes? The relation between their shapes is that all the samples have a certain fall at a particular value this is due to the reason that there was no one with that certain weight or very less people with that certain weight. Also, another relationship is that all the curves are positively skewed. It can also be said that this curves are not symmetrical because they do not follow the fall under the formula given for a normal distribution curve that is: __________ 8. What will be the relationship between their standard deviations? The only relation between the standard deviations is that the samples of the population have a class interval and also that greater the class width less is the standard deviation (i.e. scattering of data) and vice versa. 9. What causes the placement of the measures of center for the population? Why is one further to one side or the other? What is the cause?
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