1 60 30 44 1 60 example essay topic
490 words
Maths Statistics Coursework Hypotheses My first hypothesis is that on average boys are taller then girls. I obviously cannot prove this by measuring every child in the world. Instead I will take a sample of the children at Mayfield School to prove this. I also cannot check every pupil of Mayfield School, so will take a random stratified sample of 200 children. This will contain the height and averages of 102 boys and 98 girls, all ages between 11 and 16. I will first show my tally chart, which shows the ages and varying height of the children, detailing boys and girls separately. These results obviously don't prove very much, because 4/98 is a very small fraction. I will prove my hypothesis from the year-by-year mean heights. The MPV (Mid-point value) is simply the middle number in the grouped heights. The FX is the frequency column, multiplied by the mid-point value column. The totals in the F and FX are all the amounts added up.
I have calculated the mean by dividing the FX column total, by the Frequency column total. It is also interesting to note, as you go through the age groups that year-by-year the mean height is higher. The only exception to this is that 15 year old girls have a higher mean height then the 16 year old girls. I have also calculated the cumulative frequency's, for both boys and girls, separately. Cumulative Frequency: Boys Frequency Cumulative Frequency Coordinates 1.30 up to but not including 1.40 0 0 (1.4, 0) 1.40 up to but not including 1.50 14 14 (1.5, 14) 1.50 up to but not including 1.60 30 44 (1.6, 44) 1.60 up to but not including 1.70 23 67 (1.7, 67) 1.70 up to but not including 1.80 26 93 (1.8, 93) 1.80 up to but not including 2.00 9 102 (2.0,102) Totals 102 102 I have put all this information onto a graph, with the above coordinates. I have labelled the X-axis Height, and the Y-axis Cumulative Frequency.
Cumulative Frequency: Girls Frequency Cumulative Frequency Coordinates 1.25 up to but not including 1.40 4 4 (1.4, 4) 1.40 up to but not including 1.50 14 18 (1.5, 18) 1.50 up to but not including 1.60 26 44 (1.6, 44) 1.60 up to but not including 1.70 37 81 (1.7, 81) 1.70 up to but not including 1.80 15 96 (1.8, 96) 1.80 up to but not including 2.00 2 98 (2.0, 98) Totals 98 98 I have put all this information onto a graph, with the above coordinates. The Lower Quartile, Upper Quartile and Median strengthen my point, as in each case the boys Lower Quartile, Upper Quartile and Median are higher then the girls equivalent. Boys Girls Lower Quartile 1.55 m 1.525 m Upper Quartile 1.765 m 1.695 m Median 1.64 m 1.629 m.
