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  • Level: GCSE
  • Subject: Maths
  • Word count: 4947

Stratified sampling and Hypotheses - Taller people tend to be heavier - Males are taller than females - Males height is more variable than females

Extracts from this document...

Introduction

INTRODUCTION 2 Stratified Sampling Method 2 Sample 5 PLAN 8 HYPOTHESIS 1 9 Scatter graphs 9 HYPOTHESIS 2 11 Mean 12 Median 13 Grouped Frequency Tables 13 Histograms 14 Cumulative Frequency 16 Stem and Leaf Diagram 17 Relative Frequency 18 HYPOTHESIS 3 19 Range 19 Sample Standard Deviation 19 CONCLUSION 22 INTRODUCTION For this investigation, I was given a collection of data with 328 records. These records were of students with certain details about themselves. These details included: - Mathematics Set - Height (cm) - Weight (kg) - Shoe size - Hand span size I realized that this database containing 328 records of students was too large to work with. Therefore I decided to create a sample of this database using the stratified sampling method. Stratified Sampling Method Firstly, I counted the total number of male and female students in each math's set. I used a tally chart to help me with this: Math's Set Male Female Red Mauve Blue Green I then counted each tally to receive the following numbers: Red: 58 male, 65 female Mauve: 31 male, 40 female Blue: 53 male, 63 female Green: 12 male, 5 female Once I finished counting the number male and female students from each math's set, I added up all my results: 56 65 32 40 53 63 12 + 5 328 The reason I added all my results together is because if all the results added together did not equal 328, I would have not counted properly and missed students out because the total number of students is 328. I then calculated the percentage of the male and female students of each category out of the total 328 students: Percentage of Red Males 56 328 To the nearest whole number = 17% Percentage of Red Females 65 328 To the nearest whole number = 20% Percentage of Mauve Males 32 328 To the nearest whole number = 10% Percentage of Mauve Females 40 328 To the nearest whole number = 12% Percentage of ...read more.

Middle

I then divided this number by the number of numbers to receive a mean value for the height of the males. I use the same process to work out the mean value for the height the females from the sample. As you can see, the mean figure that I obtained for the male height is 173cm to the nearest whole number. The mean figure that I obtained from the female height is 165cm to the nearest whole number. The mean height value of the males is greater than the mean height value of the females by 8cm. These calculations show that on average, males are 8cm taller than females from the sample. Median Median - Males 150, 150, 160, 160, 162, 165, 165, 166, 169, 169, 170, 170, 170, 170, 170, 170, 172, 172, 172, 172, 172, 172.5, 173, 173.75, 174, 174, 174, 175, 175, 175, 176, 177, 177.5, 178, 178, 178, 179, 179.1, 180, 180, 180, 180, 181, 184, 185, 185, 190 Median = 173.75cm Median - Females 147, 150, 155, 155, 155, 155, 158, 158, 159, 160, 160, 160, 160, 160, 160, 160, 160, 162, 162, 162, 162.5, 162.5, 163, 163, 163, 163, 163, 163, 165, 165, 165, 165, 165, 165, 165, 166, 166, 167, 167, 168, 168, 169, 170, 170, 173, 173, 174, 175, 175, 177, 178.5, 180, 187 Median = 163cm As you can see from these calculations, I ordered all the different heights of the males from smallest to largest. I then searched for the middle value from the ordered list to find the median of the height of males. The number that I targeted to be the middle value for the male heights was 173.75cm. I used the same approach to find the median value of the female heights and the number I received was 163cm. The median of the female heights is lower than the median of the male heights by 10.25cm. ...read more.

Conclusion

Once I receive this number, I must find the square root of it: Standard Deviation = 2952.2444 46 Standard Deviation = 64.179 Standard Deviation = 8.011 (3d.p) After making various different calculations, I now have a standard deviation for the height of males. Using the same approach, I calculated the standard deviation for the height of females: Females Standard Deviation = 7.432 (3d.p) Now that I have two separate standard deviations for the height of males and females, we can compare the variability. As you can see, the standard deviation of the male heights is slightly greater than the standard deviation of the female heights. This shows that the males have a more variable spread of heights from the sample than the females. The female heights vary slightly less in comparison to the male heights because the standard deviation of the female heights is lower than the standard deviation of the males. Even though the range of the both male and female height was the same, the heights of males varied more than the female in the same scope of 40cm. Therefore, I must finally come to substantial conclusion. Based on these calculations, my third and final hypothesis has now been proven. "Males height is more variable than females" CONCLUSION Carrying out extensive calculations and with the assistance of very useful diagrams, I proved all three of my hypotheses. However, the hypotheses were only proven using a small sample. The rest of the characteristics of the database of student could be slightly different. This could defy all three of my hypotheses. If was given more time, I would try using a larger sample. This would provide me with more accurate results and the conclusions that I would make would be more valid in relation to the whole database, not just the sample. I would also try different sampling methods. I would then be able to support my hypotheses even further by making calculations relating to all 3 hypotheses using a number of different samples. ...read more.

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