Statistics 1

Statistics:

Introduction:

This study analysis the relationship between natural eye color, gender and the length of the index figure, it was undertaken on a sample of college students plus the staff of the college.

Method:

The total population was established to be 11, 394 and due to time limitations we decided to come up with a random sample of 120 respondents, the sample was therefore 1% of the population and there was a need to ensure consistent of data, data was collected using questionnaire where volunteer participants were to state their age, gender and the research respondent would measure the length of the index figure and record it in the participants questionnaire, data was then recoded in an excel worksheet for the purpose of statistical analysis.

Summary of data collected:

Gender:

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Of the 120 participants 68 were male while 52 were female, this means that 43% were female while 57% of the respondents were male; the chart below describes the distribution of our population:

The data was further analyzed according to age groups, this included the age group 16 to 18 years, 19 and above years and finally the staff, this age group would help establish the distribution of the sample, from the data it was also noted that among the male participants 21 were between the age group 16 to 18 years, 42 participants were 19 and above old while only 5 were staff members, the chart below summarizes this observation:

Among the female mebers 18 participants are aged between 16 and 18 years, 30 were 19 plus years old while only 4 were staff members, the chart below summarises this observation:

Index fingure length:

We also analysed the mean length for ech group, it was evident that participants aged between 16 to 18 years had a large mean length, it was evident that the staff mean length was the lowest, this signifies that as the individual grow the length of their index fingure declines, the chart below summarises the mean values for each age group:

Natural eye color:

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Of the 120 participants 42 had blue natural eye color, 12 had green natural eye color, 48 had brown natural eye color while only 20 had hazel natural eye color, this means that the majority of the respondents had brown natural eye color.

Results:

The table below summarizes the figure length mean for male and female; it also contains the median, standard deviation, maximum value, minimum value and the variance

index  figure length

male

female

mean

75.42029

71.92453

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standard  deviation

6.283512

6.284441

variance

39.48252

39.49419

median

76

71

max

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90

89

min

54

59

mode

76

71

Distribution:

Using the median, the mean and the max and minimum value we can determine the distribution

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form for male and female regarding length of the index figure. The mean length of the index figure is 75.42, the median is 76, the maximum value is 90 and the minimum value is 54, for the female the men value is 71.92 standard deviation is 6.28, the median is 71 and the maximum and minimum values are 89 and 59 respectively, according to the mean values it is evident that the mean value of males is greater than the mean value of female, according to the table it is also clear that the standard deviation value is relatively equal for both male and female.

When the mean, mode and median are equal then we refer to such a distribution as a normal distribution, in the male distribution the mode and median are equal but the mean is not equal to the mode, for the female case the median and mode are equal but the mean is not equal to the mode, however due to errors associated with samples the difference in the mean and the mode are slight in both cases and therefore we can conclude that in both cases there is a normal distribution.

Male and female values:

The mean value for the male is greater than that of the female, it is also evident that the median value for the male is greater than that of the female, however the standard deviation value for the male and female are approximately equal, a similarity between the two is that they both have normal distributions.

Regarding eye color the following chart summarizes the results of the totals in both cases in terms of percentage values:

Blue

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Green

Brown

hazel

male

38%

12%

39%

12%

female

30%

8%

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40%

23%

From the above table it is clear that majority of male have brown eyes, majority of women also have brown eyes, however according to this sample more females have hazel eyes which is 23% compared to 12% of male, less females compared to males have green eyes with only 8% of the females havng green eyes while 12% of the male having green eyes. This data can be summarized in a chart as follows:

Inter quartile range:

According to the excel output the following table summarizes the quartiles, however the interquartile range can be determined by subtracting the first quartile from the third quartile as follows:

77–70=7

The interquartile range is therefore 7

1st quartile

70

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2

73.5

3rd

77

4th

90

nd

(median)

Standard deviation and variance for the entire data:

The table below sumarises the standard deviation and variance for the entire data collected on the sample, the mean value is 73.901, the variance is 42.188 and the standard deviation is 6.49. according to the central limit theory as the number of random independent variables increase then the distribution of their sum tend to be normally distributed, this means that 95% of the observations will lie between 2 standard deviations, in this case we tend to investigate if this is true with our case, the values from our data can be summarized below:

mean

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73.901639

variance

42.188592

standard deviation

6.4952746

median

73.5

mode

71

Normal distributions have equal mean, median and mode, in our case non of this is true and for

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this reason we conclude that our distribution is not normally distributed, for this reason therefore the 95% of information being 2X standard deviation does not apply.

Conclusion:

Given the entire data it is clear that it is not normally distributed, however when we consider female and male separately then we find out that in both case it is a normal distribution. It is also clear that the males have longer index figure compared to the females, however there is aneed to undertake a similar study using a different or larger sample to check the consistency of the findings in this reaserch, this will aid in better explanation of the relationship that exist between the variable.

Hypothesis test:

Hypothesis:

Male index figure is longer than that for the female

Null hypothesis:

H0: b1 =b2 or b1 –b2 = 0

Where b1 is the mean for the males and b2 is the mean for the females

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Alternative hypothesis:

Ha : b1≠ b2

We then get our t calculated and t statistics at 5% level of test.

T calculated = (b1 –b2)/ (Sb1/n + sdb2/n)½

B1 – b2 = 3.495762

(Sb1/n + sdb2/n)½ = 0.320961

(b1 –b2)/ (Sb1/n + sdb2/n)½ = 10.89154

Because our T calculated is greater than T critical at 5% we reject the null hypothesis, by rejecting the null hypothesis we are stating that b1≠ b2 or b1 > b2. For this reason therefore we can conclude that inex figure for male are longer than those of female.

References:

Allan Bluman (2000) Elementary Statistics: A Step by Step Approach, McGraw Hill press, New York

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Daniel Bridge (1993) Statistics: An Introduction to Quantitative Research, Rand McNally publishers, Michigan

Lind and Mason (2003) Statistical Techniques in Business, McGraw Hill, New York

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