Tables for Height & Weights
I need a more useful representation of this data. Here are frequency tables for weight and height separated into boys and girls.
Boys
The above is a frequency table of the height and weight of Boys.
Girls
The above is the height and weight which has been put into a frequency table for girls.
I could now make a statement to compare the weight of boys and girls.
‘The mode shows that boy’s weight in my sample was higher than girls. Therefore there will be fewer boys weighing from 20kg to 50kg’.
Graphs for Height & Weight
Since the data is grouped into class intervals, it also makes sense to record it in a stem and leaf diagram. This will make it easier to read off the median values. I will use the following information which is stem leaf diagrams and frequency density table.
Boys, Height:
I could analyse the data about height in exactly the same way as the weight because height and weight is continuous, so you need to record it on a histogram.
I can compare continuous data by drawing the frequency polygons on the same graph.
Boys, Weight:
I will be able to find the same information in the following histogram,
I can compare continuous data by drawing the frequency polygons on the same graph.
Girls, Height:
I can compare continuous data by drawing the frequency polygons on the same graph.
Girls, Weight:
I can compare continuous data by drawing the frequency polygons on the same graph.
I am now going to show the mean, mode median and range for each of the results of the boy’s and girl’s height and weight.
Height
Mean Height
I calculate the mean easily from the frequency tables.
Mean Height for boys = 161.0
Mean Height for girls = 162.3
Modal Height
I read the modes of the height for boys and girls from the frequency table.
Modal Height for boys = 1.50≤h<1.60
Modal Height for girls = 1.60≤h<1.70
Median Height
There were 30 people in each sample, so the median will be halfway between the 15th and 16th values.
Median Height for boys = 1.615 (m)
Median Height for girls = 1.615 (m)
Range Height
The range of the height will show you how spread your data is
Range for Height for boys = 0.56(m)
Range for Height for girls = 0.60(m)
Weight
Mean Weight
I calculate the mean easily from the frequency tables.
Mean Weight for boys = 53.3(kg)
Mean Weight for girls = 50.3(kg)
Modal Weight
I read the modes of the height for boys and girls from the frequency table.
Modal Weight for boys = 40≤w<50
Modal Weight for girls = 40≤w<50
Median Weight
There were 30 people in each sample, so the median will be halfway between the 15th and 16th values.
Median Weight for boys = 50(kg)
Median Weight for girls = 47(kg)
Range Weight
The range of shoe sizes will show you how spread your data is
Range for Weight for boys = 52(kg)
Range for Weight for girls = 44(kg)
I now have more evidence to describe the difference in weight between boys and girls.
All three measures of average (mean, median and mode) are greater for boys than for girls. In conclusion, although there are a small number of boys who weighed light and girls who weighed heavy, the evidence suggests that in general, the weight for boys are greater than the weight for girls.
Extending the investigation
I can now extend the line of enquiry and give myself a hypothesis to test.
In general it is that when the height increases so does the weight.
To test this hypothesis we need a new random sample of 30 students of any gender.
Second Sample
I have now collected a second sample to extend my line of investigation that there is a correlation with height and weight between boys and girls
Boys
Girls
I am now going to make the information easier for myself to understand by putting the data into stem and leaf diagram, histograms and frequency polygons.
Boys
Height
The above is the height of boys put into a histogram and a frequency polygon to make it easier understand the data recorded
Weight
The above is data recorded for the weight for boy’s height and weight. They have been put into a histogram and a frequency.
Girls
Height
The above is a frequency table, frequency polygon and a histogram of the Height of the girls.
Weight
The above data is a histogram, frequency table and a frequency polygon for the girl’s weight.
Here are the mean, mode, median and range for the second set of data which I collected.
The most sensible way to compare this data is in the following Frequency Polygon.
From the above data I can see that there is a similarity in the relationship between the weight of boys and girls. The relationship is according to my prediction.
In the above data I can see that there is a similarity between the heights of both genders.
For the second sample of height and weight of both boys and girls I am going to put the information into a stem and leaf diagram.
Stem and Leaf diagram for Boys and Girls, Height:
Stem and Leaf diagram for Boys and Girls, Weight:
Mixed random selection of boys and girls
I will now extend my investigation further to show that the results are similar for any sample chosen at random
Scatter diagram for height and weight
Summarizing My Results
Here is a summary of some of the findings from this investigation:
- There is a positive correlation between height and weight. In general the taller the person the more he will weight and the shorter the person the smaller the weight.
- The points on the scatter diagrams for boys are less dispersed than the points on the scatter graph for the mixed sample. Of boys and girls. This suggests that the correlation between height and weight is better when boys and girls are considered separately.
- The scatter graphs can be used to give reasonable estimates of weight and height. This can be done either by reading from the graph or by using equations of lines of best fit.
- The median weight for boys is higher than the median weight for girls.
- I could have had a greater confidence in our results if I had taken larger samples or given some consideration to the ages of the students in the sample.
- My predictions are based on general trends observed in the data. In both samples there were exceptional individuals whose results fell outside the general tend.
Conclusion:
Based on the evidence that I have found and my hypothesis I say that when the height increases so will the weight. And there are many restrictions that I took part in such as gender and age and both of these has helped me to conclude this project by saying the height and weight depend on gender and age, by this I am saying that the height and weight will increase depending on the gender and age.
If I were to the investigation again I would consider the height and weight in more detail and have a greater sample of both genders.
I have proved that there is a positive correlation between the height and weight of both male and females.