Total number of boys/girls
Total number of pupils in year x sample size
Boys- 209 x 50
404
= 25.86
26 boys
Girls- 195 x 50
404
= 24.13
24 girls
For my sample I will be using 26 boys and 24 girls.
Now I will use stratified random sampling to define which students I will be using in my sample.
Boys
061 700 739 407 978 013 554 486 076 685 519 428 273 580 055 836 992 655 830 385 236 463 914 172 664 539
I will now use the remainder method because over half my numbers are over 209.
Multiples of 209 are 209
418
627
836
700 = 3r 73 I will use 073
739 = 3r 112 I will use 112
407 = 1r 198 I will use 198
978
554 = 2r 136 I will use 136
486 = 1r 141 I will use 141
685 = 3r 58 I will use 058
519 = 2r 101 I will use 101
428 = 2r 10 I will use 010
273 = 1r 64 I will use 064
580 = 2r 162 I will use 162
836 = 4r 00 I will use 000
992
655 = 3r 28 I will use 028
830 = 3r 203 I will use 203
385 = 1r 176 I will use 176
236 = 1r 27 I will use 027
463 = 2r 45 I will use 045
914
664 = 3r 37 I will use 037
539 = 2r 121 I will use 121
3 of my numbers were above 836 so they were to high to use, I will return to stratified random sampling to get 3 more numbers and then use the remainder method to make them useful.
246 = 2r 172 I will use 172
075 = 1r 134 I will use 134
167 = 1r 42 I will use 042
I now have my sample for the boys it is:
061 013 076 055 172 073 064 198 136 068 058 101 010 045 162 000 028 203 176 027 037 121 172 134 042 112
Girls
I will use the stratified random sampling method to pick 24 numbers for the girls sample.
140 430 463 509 976 982 811 159 712 379 711 376 933 173 693 317 385 703 530 297 608 194 324 663
I will now use the remainder method so all of the numbers I picked can be of a use.
Multiples of 195 are 195
390
585
780
975
430 = 2r 40 I will use 040
463 = 2r 73 I will use 073
509 = 2r 119 I will use 119
976
982
811 = 4r 31 I will use 031
712 = 3r 127 I will use 127
379 = 1r 184 I will use 184
711 = 3r 126 I will use 162
376 = 1r 14 I will use 014
933 = 4r 153 I will use 153
693 = 3 r 108 I will use 108
317 = 1r 122 I will use 122
385 = 1r 190 I will use 190
703 = 3r 118 I will use 118
530 = 2r 140 I will use 140
297 = 1r 102 I will use 102
608 = 3r 23 I will use 023
324 = 1r 129 I will use 129
663 = 3r 78 I will use 078
2 of my numbers are too high, so I will go back to stratified random sampling and then to the remainder method so the numbers would become useful.
223 = 1r 28 I will use 028
544 = 2r 154 I will use 154
I now have a sample for the girls it is:
149 119 153 040 118 129 073 014 194 140 184 078 126 173 127 102 122 154 159 031 108 023 190 028
Averages
Shoe sizes
To show shoe sizes I will work out averages and will do a pie chart for both male and female pupils in year 11.
Boys shoe sizes
Mode = Size 8
Mean = 5 + 6 + (6.5 x 3) + (7 x 3) + 7.5 +(8 x 9) + (8.5 x 2) + (9 x 2) + (10 x 4)
26
= 8.0
= Size 8
Median = 5 6 6.5 6.5 6.5 7 7 7 7.5 8 8 8 8 8 8 8 8 8 8.5 8.5 9 9 10 10 10 10
= Size 8
Girls shoe sizes
Mode = Size 6
Mean = 3 + 3.5 + (4 x 3) + 4.5 + (5 x 3) + 5.5 + (6 x 8) + 6.5 + (7 x 3) + 7.5 + 8
24
= 5.6
= Size 5.5
Median = 3 3.5 4 4 4 4.5 5 5 5 5.5 6 6 6 6 6 6 6 6 6.5 7 7 7 7.5 8
= Size 6
For shoe sizes I would think mode is the best way to display the data because it shows which size shoe is actually the most popular.
Pie Charts
Shoe Sizes
Boys
*See pie chart on next page
Histograms
Weights
To show weight for boys and girls in year 11 I will draw histograms, which will show the data in both the height of the bar but also in the area.
Boys
*See graph on next page
Girls
* See graph on next page
Scatter Diagram
Height Compared to Shoe Size
Boys
Girls
*See graph on next page
Cumulative Frequency
Heights
Boys
*See graph on next page
*See graph on next page
Inter-quartile Range
Upper quartile – Lower quartile = Inter-quartile Range
Boys
173 – 166 = 7
Girls
167 – 155 = 12
Standard Diviation
Armspan
I will use standard diviation because it will show a good spread of data unlike the inter-quartile range because it uses all the data.
Standard diviation = √∑(x − x) = √1642.36
.n 26
= 7.9 (1.d.p)
Percentages and Bar Graphs
Can/Cannot Swim, Left/Right Handed and Can/Cannot Roll Tongue
I will use percentages to display the amount of pupils in year 11 who can or cannot do the things above. These results will be shown in a bar graph and will be done for both boys and girls.
Boys – swimming
Girls – swimming
Boys – left/right handed
Girls – left/right handed
Boys – Rolling tongue
Girls – Rolling tongue
Conclusion
After carrying out this investigation, I found the following points:
- Males are taller generally than females and most of the time have a bigger shoe size
- Boys mainly do weigh more than girls then the data is not more evenly spread out as I predicted.
- More people can swim compared to the amount that cannot
- More pupils in year 11 are right handed, and more boys are right handed (92%) to the amount of girls (83%)
- The percentage of pupils who can roll their tongue is greater then those who cannot, but it seem to be more dominant in boys
