• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month
Page
  1. 1
    1
  2. 2
    2
  3. 3
    3
  4. 4
    4
  5. 5
    5
  6. 6
    6
  7. 7
    7
  8. 8
    8

Statistical Analysis of Facial Proportions

Extracts from this document...

Introduction

Maths coursework Statistical Analysis of Facial Proportions The coursework task that I am following is S1 Task A. The aim of my investigation is to find how beautiful the year seven pupils are in my school, according to Pythagoras' Theory that the more beautiful a person is, the closer the measurements of certain features of the body, to the ratio of 1:1.618. The samples that I will take will be random samples of males and females in year seven. The samples will be taken in the following way. Each of the pupils in year seven has a number next to their name in the teachers' register. I will select random numbers using the random number generator facility on my graphic calculator, and the numbers that match up with the names on the register will be selected from the population and the submitted to the analysis. I will select 25 people from the register at random and submit the same people to both measurements. If the same number is selected again, I will take the next random number as the next person for analysis. The measurements that I will be taking will be: 1. ...read more.

Middle

Proximal Central Ratio Proximal Central Ratio 5 3.1 1.613 4.5 3.4 1.324 5.5 3.2 1.719 5.2 3.1 1.677 3.6 2.4 1.5 4.5 3 1.5 3.4 2.9 1.172 4.5 2.5 1.8 3.2 2.4 1.333 3.5 3 1.167 5 3 1.667 5.3 0.2 1.656 4.4 3 1.467 4 2.8 1.429 4 2.5 1.6 4 2.5 1.6 3.7 2 1.85 3.5 2.8 1.25 3.4 2.8 1.214 3.8 3 1.267 4.1 2.8 1.464 4.8 3.1 1.548 3.7 3 1.233 4.5 3 1.5 5.1 2.9 1.759 3.5 2.5 1.4 4 2 2 4.1 3.2 1.281 3.5 2 1.75 4.6 2.7 1.704 4.5 2.1 2.143 5 32 1.563 4.5 2 2.25 4.8 3.1 1.548 4.8 2.5 1.92 4.7 3.2 1.469 3.7 2.5 1.48 4.2 3 1.4 4.2 3.8 1.105 4.4 3.2 1.375 4.6 3.3 1.394 5 2.9 1.724 4.2 3 1.4 5 3.6 1.389 4.6 3 1.533 4.5 2.7 1.667 4.7 2.9 1.621 4.8 3 1.6 5.8 3.3 1.758 4.7 2.9 1.621 Measurements of the Mouth and Nose Ratios. Males The sample mean = 1.606 The sample variance = 0.093 Females The sample mean = 1.603 The sample variance = 0.067 Since the samples are random, the distribution of the sample means are equals to the actual populations being estimated. ...read more.

Conclusion

Males The sample mean = 1.598 The sample variance = 0.086 Females The sample mean = 1.498 The sample variance = 0.028 Since the samples are random, the distribution of the sample means are equals to the actual populations being estimated. Therefore can be used to estimate the parent population. Males Unbiased estimate of the Population mean = 1.598 Females Unbiased estimate of the Population mean = 1.498 However, the sample variance is a biased estimator of the population variance. To convert this to an unbiased estimator, this method was used; If S squared is the sample variance of a sample size n then, x S squared is an unbiased estimator of the population variance. Males Unbiased estimate of the population variance = 25 x 0.086 24 = 0.090 Females Unbiased estimate of The population variance = 25 x 0.028 24 = 0.029 Therefore for the whole population: Males X ~ N (1.598,0.086) Females X ~ N (1.498,0.029) To compare these results, I will calculate 95% Confidence intervals for males and females, and compare the size of the interval. I will also compare where the intervals lie in relation to each other. Males: X ~ N (1.598,0.086) Females: X ~ N (1.498,0.029) Placing of confidence intervals. Males Females ...read more.

The above preview is unformatted text

This student written piece of work is one of many that can be found in our AS and A Level Probability & Statistics section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related AS and A Level Probability & Statistics essays

  1. Marked by a teacher

    The heights of 16-18 year old young adults varies between males and females. My ...

    5 star(s)

    = 1.6449 ?² n-1 ( n ) S² n-1 = 50 x 9.13 = 9.316 49 µ = ± x ? n-1 V n µ = 70.1 ± 1.6449 x 9.316² V 50 µ = 70.1 ± 1.6449 x V 9.316 7.071 µ = 70.1 ± 1.6449 x 3.052

  2. The mathematical genii apply their Statistical Wizardry to Basketball

    It also allows me to use the chi squared test on the model to check if there is any evidence to suggest that one thrower is better than the other at various critical levels.

  1. Statistics Coursework

    87.57 120 92.86 167 96.56 214 99.47 27 78.84 74 87.57 121 93.12 168 96.56 215 99.47 28 79.1 75 87.83 122 93.12 169 96.56 216 99.47 29 79.89 76 87.83 113 93.65 170 96.83 217 99.47 30 79.89 77 87.83 124 93.65 171 96.83 218 99.47 31 80.16 78

  2. How Can Samples Describe Populations?

    In order to attain a random selection some mechanism ensures that each subject in the sample frame has an equal probability of being chosen as the rest of the population. Random selection can be as simple as picking a name out of a hat, or choosing the short straw.

  1. Statistics coursework

    I had completed this graph I realised it wasn't a true and accurate reflection of the year 7's IQs due to there being a different number of boys and girls in the year group. This meant any comparisons could be affected by the strata size.

  2. DATA HANDLING COURSEWORK

    Weight (kg) (up to and including) Tally Frequency 0 - 10 0 11 - 20 0 21 - 30 0 31 - 40 I 1 41 - 50 IIIIIIIIIIIIIIII 16 51 - 60 IIIIIIIII 9 61 - 70 III 3 71 - 80 I 1 81 - 90 0 91 - 100 0 I will now

  1. Intermediate Maths Driving Test Coursework

    Above we see a very weak negative correlation with no points lying on the line of best fit. . Again I could use this graph as further evidence for my previous hypothesis that men perform better in the test than women, but this graph could also show that instructor B teaches men better than women.

  2. Identifying Relationships -Introduction to Statistical Inference.

    16.7% (51.4%) 48.3% (51.4%) 67.6% (51.4%) 54.1% No Count 2 10 15 12 39 % within Type of Hotel 28.6% (45.9%) 83.3% (45.9%) 51.7% (45.9%) 32.4% (45.9%) 45.9% Total Count 7 12 29 37 85 % within Type of Hotel 100.0% 100.0% 100.0% 100.0% 100.0% There are three possible outcomes

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work