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Maths Statistics CourseworkHypothesesMy 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 00 children. This will contain the height and averages of 10 boys and 8 girls, all ages between 11 and 16. Help with essay on Maths - Mayfield
I will first show my tally chart, which shows the ages and varying height of the children, detailing boys and girls separately.Males Grouped Height Ages 11/1 Aged 1 Aged 14 Aged 15 Aged16 Total1.0 up to but not including 1.40 0 0 0 0 0 01.40 up to but not including 1.45 0 0 0 51.45 up to but not including 1.50 7 1 1 0 0 1.50 up to but not including 1.55 7 4 171.55 up to but not including 1.60 4 1 5 0 11.60 up to but not including 1.65 6 1 11.65 up to but not including 1.70 0 4 1 101.70 up to but not including 1.75 0 6 6 4 181.75 up to but not including 1.80 0 1 81.80 up to but not including 1.0 0 1 0 51.0 up to and including .00 0 0 1 1 4Total frequency 6 6 14 14 10 Females Grouped Height Ages 11/1 Aged 1 Aged 14 Aged 15 Aged16+ Total1.0 up to but not including 1.40 1 0 0 0 41.40 up to but not including 1.45 1 0 0 0 1.45 up to but not including 1.50 5 0 0 111.50 up to but not including 1.55 4 1 4 1 1 111.55 up to but not including 1.60 5 151.60 up to but not including 1.65 5 5 4 4 01.65 up to but not including 1.70 0 7 6 171.70 up to but not including 1.75 1 1.75 up to but not including 1.80 1 1 0 61.80 up to but not including 1.0 0 0 0 0 Total frequency 5 1 18 1 8 All grouped data 00 From this it is noticeable that boys are taller then girls, as there are no boys, of any age, who are shorter then 1.40m, yet there are 4 girls who are below this mark, aged 11-1. These results obviously don't prove very much, because 4/8 is a very small fraction.I will prove my hypothesis from the year-by-year mean heights.Females Ages 11/1 Grouped height F MPV FX MEAN1.0 up to but not including 1.40 1.0 . 1.40 up to but not including 1.50 7 1.45 10.15 1.50 up to but not including 1.60 6 1.55 . 1.60 up to but not including 1.70 5 1.65 8.5 1.70 up to but not including 1.80 4 1.75 7 1.80 up to but not including .00 0 1.0 0 Totals 5 4.7 1.88 Aged 1 Grouped height F MPV FX MEAN1.0 up to but not including 1.40 1 1.0 1. 1.40 up to but not including 1.50 4 1.45 5.8 1.50 up to but not including 1.60 4 1.55 6. 1.60 up to but not including 1.70 7 1.65 11.55 1.70 up to but not including 1.80 1.75 5.5 1.80 up to but not including .00 0 1.0 0 Totals 1 8.8 1.51578 Aged 14 Grouped height F MPV FX MEAN1.0 up to but not including 1.40 0 1.0 0 1.40 up to but not including 1.50 1.45 4.5 1.50 up to but not including 1.60 7 1.55 10.85 1.60 up to but not including 1.70 11 1.65 18.15 1.70 up to but not including 1.80 1.75 .5 1.80 up to but not including .00 0 1.0 0 Totals 6.85 1.60174 Aged 15 Grouped height F MPV FX MEAN1.0 up to but not including 1.40 0 1.0 0 1.40 up to but not including 1.50 0 1.45 0 1.50 up to but not including 1.60 6 1.55 . 1.60 up to but not including 1.70 6 1.65 . 1.70 up to but not including 1.80 4 1.75 7 1.80 up to but not including .00 1.0 .8 Totals 18 0 1.666667 Aged 16+ Grouped height F MPV FX MEAN1.0 up to but not including 1.40 0 1.0 0 1.40 up to but not including 1.50 0 1.45 0 1.50 up to but not including 1.60 1.55 4.65 1.60 up to but not including 1.70 8 1.65 1. 1.70 up to but not including 1.80 1.75 .5 1.80 up to but not including .00 0 1.0 0 Totals 1 1.5 1.6408 Males Ages 11/1 Grouped height F MPV FX MEAN1.0 up to but not including 1.40 0 1.5 0 1.40 up to but not including 1.50 10 1.45 14.5 1.50 up to but not including 1.60 10 1.55 15.5 1.60 up to but not including 1.70 6 1.65 . 1.70 up to but not including 1.80 0 1.75 0 1.80 up to but not including .00 0 1.85 0 Totals 6 . 1.54615 Aged 1 Grouped height F MPV FX MEAN1.0 up to but not including 1.40 0 1.5 0 1.40 up to but not including 1.50 1.45 4.5 1.50 up to but not including 1.60 8 1.55 1.4 1.60 up to but not including 1.70 6 1.65 . 1.70 up to but not including 1.80 8 1.75 14 1.80 up to but not including .00 1 1.85 1.85 Totals 6 4.5 1.64615 Aged 14 Grouped height F MPV FX MEAN1.0 up to but not including 1.40 0 1.5 0 1.40 up to but not including 1.50 1 1.45 1.45 1.50 up to but not including 1.60 1.55 4.65 1.60 up to but not including 1.70 5 1.65 8.5 1.70 up to but not including 1.80 1.75 15.75 1.80 up to but not including .00 4 1.85 7.4 Totals 7.5 1.704545 Aged 15 Grouped height F MPV FX MEAN1.0 up to but not including 1.40 0 1.5 0 1.40 up to but not including 1.50 0 1.45 0 1.50 up to but not including 1.60 7 1.55 10.85 1.60 up to but not including 1.70 1.65 . 1.70 up to but not including 1.80 4 1.75 7 1.80 up to but not including .00 1 1.85 1.85 Totals 14 1.64857 Aged 16 Grouped height F MPV FX MEAN1.0 up to but not including 1.40 0 1.5 0 1.40 up to but not including 1.50 0 1.45 0 1.50 up to but not including 1.60 1.55 .1 1.60 up to but not including 1.70 4 1.65 6.6 1.70 up to but not including 1.80 5 1.75 8.75 1.80 up to but not including .00 1.85 5.55 Totals 14 4 1.71486In these tables I have calculated a number of thingsThe frequency is the amount of times that height occurs.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.Total means 11/1 1 14 15 16 Average meansMales 1.546 1.646 1.7045 1.64 1.714 1.646Females 1.880 1.5158 1.60 1.6667 1.64 1.560 As you can see from the year-by-year means every male age group has a higher mean height, then there female equivalents. 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 Coordinates1.0 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 0 44 (1.6, 44)1.60 up to but not including 1.70 67 (1.7, 67)1.70 up to but not including 1.80 6 (1.8, )1.80 up to but not including .00 10 (.0, 10) Totals 10 10 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.I have also calculatedLower Quartile = ¼ n = ¼ (10) = 5.5th value = 1.55m Upper Quartile = ¾ n = ¾ (10) = 76.5th value = 1.765mMedian = ½ n = ½ (10) = 51st value = 1.64mThese are also marked out on the graph.Cumulative Frequency Girls Frequency Cumulative Frequency Coordinates1.5 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 6 44 (1.6, 44)1.60 up to but not including 1.70 7 81 (1.7, 81)1.70 up to but not including 1.80 15 6 (1.8,6)1.80 up to but not including .00 8 (.0, 8) Totals 8 8 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.I have also calculatedLower Quartile = ¼ n = ¼ (8) = 6.5th value = 1.55m Upper Quartile = ¾ n = ¾ (8) = 7.5th value = 1.65mMedian = ½ n = ½ (8) = 4th value = 1.6mThese are also marked out on the graph.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 1.55m 1.55mUpper Quartile 1.765m 1.65mMedian 1.64m 1.6m
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