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# Math Portfolio Type I

Extracts from this document...

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)

Middle

62

6

372

63

0

64

5

320

65

6

390

66

1

66

67

1

67

68

2

136

69

0

70

3

210

71

1

71

72

1

72

73

3

219

74

0

75

1

75

76

1

76

77

1

77

78

2

156

79

1

79

80

1

80

81

1

81

82

0

83

0

84

2

168

85

0

86

0

87

0

88

0

89

0

90

3

270

91

0

92

0

93

0

94

0

95

1

95

96

0

97

0

98

1

98

99

0

100

0

After obtaining this table I calculated the mean, median, mode and standard deviation for this sample of population.

First the mean was calculated (µ) by using the following formula:

µ = (∑fixi)/fi

Where,

µ: Mean

fi: Frequency

xi: Weight of students

∑: Sum total all the fi( frequency) and xi (weight)

Hence, the mean (µ) obtained was:  60.59

After calculating the mean (µ) then the median (M) was found by using the following formula:

[(n+1)/2]

Where,

M: Median

n: Sum total of number of students

Hence, the median (∂) obtained was 50.5

After calculating the median (∂) the mode was found.

This was done by just looking at the table and seeing the highest frequency which is marked with yellow on the table it self. (i.e. 50)

Lastly, the standard deviation (σ) by using “STDEV (: ; : )” on the Microsoft Excel Sheet.

Hence, the standard deviation (σ) obtained was 35.17023617

After finding the mean, median, mode and standard deviation for the 100 weights, the same but this time by taking two different class intervals (i.e. 10 & 5) was calculated.

The first one class interval taken was of 10. In the table a class interval of 10 (C.I), the middle value of the class interval range (xi), frequency (fi) and the product of the middle value and the frequency (fixi)

Conclusion

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.

1. 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:

__________

1. 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.

1. 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?

This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.

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