I have done this over 40 times and here are my results
All my chosen pupils have been put in order for easier reference, starting from year 7 down to year 11.
WHAT I HAVE FOUND OUT
In my results, I found out that my prediction was wrong, as the weight has varied in some of the year groups. Therefore, the person can be any age and they can have different weights.
TALLY FOR BOTH GIRLS AND BOYS TOGETHER
WEIGHT FREQUENCY TABLES
HEIGHT FREQUENCY TABLES
WEIGHT FREQUENCY GRAPH (kg)
HEIGHT FREQUENCY GRAPH
Now I will join both the girls and the boys weight results and compare them.
BOYS AND GIRLS WEIGHT FREQUENCY GRAPH
The chart shows that the girls are significantly heavier than the boys until, after 50 kilograms, when the boys suddenly start gaining more weight. I predict that the weight increase of the boys will also affect their height as well.
BOYS AND GIRLS HEIGHT FREQUENCY GRAPH
EVALUATION
Once again, I was right into thinking that the height of the girls would steadily go up and collapse. The boys’ heights have steadily gone up and eventually come down steadily, although there was a more free fall as it came down after reaching 1.70 to 1.79 meters.
CONCLUSION
My conclusion is that boys grow taller and they gain more weight as they grow older. In year 7 both sexes were relatively, the same height and the same weight and as they grew older the boys had a much bigger increase in weight and height.
CALCULATING THE MEAN, MODE, MEDIAN AND RANGE OF MY RESULTS.
MEAN
Calculating the mean is actually easy. If f is the frequency and x is the weight or the height then the mean is ∑fx/∑f.
First, I will calculate the mean for all forty samples then I will separate them into different sexes. Through my teacher, I have found out a method of calculating my mean. The method only gives me the estimated weight but I think that is good enough, as I had no other way to do it.
Then I added all the results I got in the F (x) and my result was 2015. Then I divided this result by frequency (f) which was 40 students so
Est. mean = ∑fx/∑f = 2015/40 = 50.375
Weight: estimated mean = 50 kg
MODE
The mode is the set of data with a value, which is the most. In my investigation, this will be very easy, as I have put them into smaller groups.
Modal value for all students is
Weight: 51 to 55kg
Height: 1.60 to 1.69 m
Modal values for boys are
Weight: 56 to 60kg
Height: 1.70 to 1.79 m
Modal values for girls are
Weight: 41 to 45kg
Height: 1.60 to 1.69m
MEDIAN
Median is one of the easiest samples to find. It is the middle value when the data is arranged in order of size.
There is an easier way to do which has the formula:
N+1/2
In which N is the input, and it is added to 1 and divided by 2
Example
There are nine values in a table
So
9+1/2= 5
In my results the modal value is
Weight: 4.5 (4,6)
Height: 3.5 (4,8)
RANGE
The range is simply the highest value subtracted by the lowest value
Height: 9-2 = 7 is the range
Weight: 13-1 = 12 is the range
INDIVIDUAL RANGES
BOYS
Weight: 5-2 = 3
Height: 8-1 = 7
GIRLS
Weight: 5-1 = 4
Height: 9-1 = 8
CONCLUSION
I think the conclusion is self-explanatory as there is no detailed calculation for this part of the course work. There is little to do for this part, but the only problems I had were with calculating the mean.
STEM AND LEAF DIAGRAMS
WEIGHT
HEIGHT
SCATTER DIAGRAMS
I will need to make scatter diagrams because I will have to plot a line of best fit. After doing this I will know how much weight is in correlation with height.
My evaluation and conclusion is that there is a gradual increase with both of the charts in weight and height. I was not expecting a very big difference with the increase and decrease in the weight.
CALCULATING THE UPPER AND LOWER QUARTILES
The inter-quartile ranges are used to determine other ranges other than the mean, median, mode and range. It is useful because it will determine a quarter and three-quarter of the results.
The formula of the inter quartile ranges are:
Lower quartile: n+1/4 (n will be the input in the equation)
Upper quartile: 3(n+1)/4
So in my table the lower quartile is:
WEIGHT:
lower quartile: 40+1/4 = 10.25 WHICH IS ROUNDED OFF = 45 kg
Upper quartile: 3(40+1)/4 = 30.75 which is also rounded off = 60 kg
SO THE INTER-QUARTILE RANGE IS
60 kg-45 kg = 15kg is the inter-quartile range
HEIGHT:
lower quartile: 40+1/4 = 10.25 WHICH IS ROUNDED OFF = 1.56m
Upper quartile: 3(40+1)/4 = 30.75 which is also rounded off = 1.73m
Range of the inter-quartiles =
1.73 – 1.56 = 0.17m.
CUMULATIVE FREQUENCY GRAPHS
These graphs are very useful because the show the flow of a chart. I am going to use this to see at what time of the pupils lives do they gain the most weight and when they increase the most height.
I think that I have been quite successful in my course work. My prediction matches my table and my frequency and I am happy with these results and feel that I have completed everything I needed to do.