55 girls in my sample of 60.23
E.g. Boys 66
60 = 32.7… 33
121
I need to choose 33 boys from 001 > 066 and 27 girls from 067 > 121.
I shall use my calculations to generate my random numbers. To do this I press the following keys:
2nd Function / Shift Random = population + round to nearest integer.
The following is my sample of 60.
Grouped frequency tables.
Unfortunately, these samples are still too large to let me look at the data clearly, so I will put them into grouped frequency tables before carrying out my calculations.
Boys
total f = 33 fx= 5642.5 fx=35580
Girls
Total f = 27 fx= fx=
One single number must be chosen to represent each group, so logically it is the mid point. That is why I have included this column. The Fx and Fx columns are included to help me find the mean length and standard deviation. I will now begin to compare the two groups’ results.
Mean
The mean is the measurement of arithmetic average. Looking back to my hypothesis, I expect that the mean height of the boys will be greater than the girls.
To find the mean height, I will use this formula:
Mean = fx
F
Mean height for boys = 5642.5 = 171 cm (nearest cm)
33
Mean for girls = = cm (nearest cm)
27
Standard deviation
Standard deviation is a measure of spread. It is the average distance of a set of numbers away from the mean. Looking back to my hypothesis, I expect that there will be a greater spread in the boys than the girls.
To find the SD, I will use the formula:
SD = Fx - fx
F f
SD boys = 35580 - 4434
33 33
SD girls= -
Histograms
A histogram is a bar chart where the area of each bar gives the number items in that category. In order to draw a histogram the frequency density must first be calculated. This is how the link between the area of each bar and the frequency it represents is achieved. To find the frequency density I will use this formula:
Frequency density = Frequency
Class width
For example, in the boys sample, the group 150<h<155 has a frequency of 2. It’s class width is 5 ( the difference between 150 and 155) therefore the frequency density = 2 = 0.4
5
I will now draw tables showing the frequency density of all the groups.
From the histograms, I can see that the boys are fare more spread out than those of the girls, as there are more bars across the range. The modal group for the boys is 165<h<170 and for the girls was 160<h<165 and 165<h<170 because the girls have to modal groups we call this bi-modal.
Conclusion
Having completed the investigation I can now conclude that there is positive correlation between height and arm span between Yr.10 pupils. The mean arm span and Height were similar. There was also a greater dispersion in the height of the boys than the girls.
Evaluation
Possible errors – how to avoid in future.
- Human error – scale read incorrectly – could avoid this by having second person to double check results.
- Height – Ensure all shoes are taken off.
- Errors in measurement – Take to nearest cm.
- Arm span – measuring length of one arm and doubling is incorrect – must ensure that everybody follows same method of measurement for consistency measure horizontal distance from left to right index finger.