I then got the number of students by:
Year 7 boys: 151xRAN#
11, 110, 123, 106, 33, 9, 55, 52.
Year 7 girls: 131xRAN+152
152,163,274,206,214,259,245
Year 8 boys: 145xRAN#+283
326,406,359,293,370,407,392
Year 8 girls: 125xRAN#+428
476,539,475,500,464,498.
Year 9 boys: 118xRAN#+553
652,594,664,634,656,568.
Year 9 girls: 143xRAN#+671
674,748,727,676,793,756,774.
Year 10 boys: 106xRAN#+814
876,860,916,820,855.
Year 10 girls: 94xRAN#+920
1005,996,987,949,923.
Year 11 boys: 84xRAN#+1014
1085,1051,1037,1044.
Year 11 girls: 86xRAN#+1098
1100,1146,1182,1127.
My students.
My first hypothesis is:
- Boys weigh more than girls.
I undertook this hypothesis by Drawing Histograms, Frequency polygon and stem and leaf diagram. From the following investigation that I undertook, the following supports or doesn’t support my hypotheses.
Mean: Boys = 55.11, Girls = 49.11. This individual investigation supports my hypotheses as the boys weight mean is higher than the girls showing me that boys weigh more than girls.
Mode: Boys = 50kg, Girls = 54kg. This doesn’t really tell us who weighs more but it tells us what weight is the most reoccurring weight in either sex and the girls have a higher reoccurring weight over boys.
Median: Boys = 50kg, Girls = 50kg. The middle weight out of the students is the same.
Histogram and frequency polygon.
The histogram shows like the polygon that my hypothesis “Boys weigh more than girls” is correct. Histograms like the polygon show that boys weigh more than girls.
When I drew the frequency polygon it shows me that boys do weigh more than girls e.g. Boys 40-45=7, whereas girls 40-45=6.
You can also see that boys continue up to 90kg whereas girls end at 60-65. This also tells us bys weigh more. However we must take into account that we have more boys than girls (31 and 28).
Stem and leaf diagram
Mode classes: Girls = 40-50, boys= 40.
Median = girls = 50, boys =50.
My hypothesis is correct.
My second hypothesis is:
- Heavier the person, taller they will be.
I undertook this hypothesis by using scatter graphs:
From the following investigation that I took, the following does or does not support my hypotheses.
Mean weight: Girls = 49.11kg, Boys = 55.11 kg.
Mean height: Girls = 1.60m, boys = 1.66 m
Mode height: Girls = 1.60 m, boys = 1.50 m/1.70m.
Mode weight: Girls = 54kg, Boys = 50kg
Median height: Girls = 1.60m, Boys = 1.63m
Median weight: Girls = 48kg, Boys = 50kg.
Point where they intercept the vertical axis and their gradient:
Boys: y=76x-71 (positive correlation, more spread out).
Girls: y=23x=13 (Low positive correlation)
Mixed: y=60x-46.
By using the equations above I can predict the weight of a boy who is 1.50m tall:
Y=76x1.50-71
= 43kg
Further to this I can predict the height of a boy who weighs 50kg:
50+71 = 121/76= 1.59m
This Equation for the boys supports my hypotheses as it shows the heavier the person the taller they will be e.g. 43kg = 1.50m, whereas 50kg = 1.59 m tall. (An increase in weight shows an increase in height).
I can now again predict the weight of a girl who is 1.50m tall.
Y=23x1.50+13
= 47.5kg
Using the same method as above I can predict the height of a girl who weighs 50kg:
50+13/23= 50.5kg
Again the equation supports my hypotheses.
My hypothesis is correct. Also by doing this investigation it also supports my third (below) hypotheses that boys are taller than girls.
My third and final hypothesis is:
- Boys are taller than girls.
For this investigation I used cumulative frequency and box plot.
Height (cm) Median *LQ* *UQ* *IR*
*LQ*- Lower quartile
*UQ*- Upper quartile
*IR* - Interquartile range.
Between boys and girls 21 students were between 140 – 160cm tall. This tells us that 7 had up to a height of 150cm, and 14 were up to 160cm tall. 14-7=7 students had the height between 140-160cm. 7
---- Students in school were between 140-160.
59
The cumulative frequency graph tells us that 11 boys had the height from140-160cm.
3 had the height from 140-150cm and 8 had the height from 150-160. 8-3=5 boys had the height between 140-160. 5
------ Boys in school are between 140-160cm.
31
The graph also tells us that 10 girls had the height from 140-160cm. 4 had the height from 140-150, and 6 had the height from 150-160cm. 6-4=2 girls had the height between 140-160cm. 1
----- Girls in school are between 140-160c tall,
14
Mean girls:
145x4= 580
155x6= 930
165x13= 2145
175x5= 875
-------
4530/28=162cm.
Mean boys:
135x1= 135
145x3= 435
155x8= 1240
165x9= 1485
175x5= 875
185x4= 740
195x1= 195
------
5105/31=165cm.
Modal class = girls-160<h<170, boys-160<h<170
Mode height= girls- 160cm, boys-150/170cm
Median: girls- 160cm, boys-163cm.
The following investigations that I undertook (above) show me that my hypothesis “Boys taller than girls” is correct. Boys go on for longer and they go up to 200cm whereas girls go up to 180cm.
Box Plot:
The box and whisker diagram show that the girl’s interquartile range is 1cm less than the boys. This tells us that the boy’s height is more spread out than the girls
.My hypotheses again has bee shown as being correct.
