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Investigatings heights of girls and boys in year seven.

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Introduction

Statistics Coursework


When standing at the station waiting for my bus home, I noticed some year seven boys from St Olaves introducing themselves to one and other. They were talking to each other about their experiences of their first week at a new school when I noticed that they were a lot smaller than I remember myself and my friends being in year seven. I then began to think about general heights of boys and girls, wondered if girls were always taller than boys. I decided to investigate this.

I predict that girls in year seven will be taller than boys in year seven.

I will attempt to either disprove or prove my hypothesis by taking the averages of heights of a sample of year seven boys and a sample of the year seven boys.

The Data I am using is Secondary, as somebody else collected it, for me. The fact that this data is Secondary can leave me with some problems. When collected the data, people may have forgotten to take their shoes off. They may have also measured in feet and inches and translated it roughly by the means of stating the one inch equals two point five centimetres. Though this is correct, the conversion from one type of measurement to another could have resulted in a loss of accuracy. People may also have added their hair into their height.

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Middle

155 ≤x> 160

8

160 ≤x> 170

4

170 ≤x> 175

0


For the Girls data, these are the frequency of the heights.

Height

Frequency

130 ≤x> 140

2

140 ≤x> 150

19

150 ≤x> 155

8

155 ≤x> 160

5

160 ≤x> 170

5

170 ≤x> 175

1


I will now use my data to draw graphs that will help me to draw conclusions from my data. In my coursework, I will include a Box and Whisker Diagram and a Histogram. I will also find Standard Deviation, the interquartile ranges and mean of my data, the range of my data and Pearson’s Correlation Coefficient.


Histogram:

As I have grouped my data in unequal class widths, I feel that a histogram would be a fairer representation of my data. This is because in a Cumulative Frequency graph, my data is represented by height rather that area, and as people tend to look at area before height, at first glance a smaller section of my Cumulative Frequency graph may appear larger than it should be. As in a Histogram the frequency density is equal to the area rather than the height, it is more representative of my data than a Cumulative Frequency graph would be.


Cumulative Frequency:

I chose to do a Cumulative Frequency graph because


Box and Whisker Diagram:

I have included a Box and Whisker Diagram in my

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Conclusion

Height

Frequency

Cumulative Frequency

130 ≤x> 140

2

2

140 ≤x> 150

19

21

150 ≤x> 155

8

29

155 ≤x> 160

5

34

160 ≤x> 170

5

39

170 ≤x> 175

1

40

I will now use the Cumulative Frequency data I have obtained to help me find PCC. The number I reach at the end of my calculations should be between minus 1 and plus one, plus one being perfect positive correlation, minus one being perfect negative correlation, and zero being no correlation at all.

My value for Pearson’s Correlation Coefficient was 0.992835. This is an almost perfect positive value for my correlation.


Second Hypothesis

I believe that the taller the girl, the larger the hand span.

I will achieve this by using the bi-variate data that I have to create a scatter graph and draw conclusions from the correlation. I will use the sample of fifty girls that I have already taken, and used for my first hypothesis.


Conclusion:

I conclude that year seven boys are taller than year seven girls. This is if I compare the means of the two data sets. They are however, only slightly taller than year seven girls, by 10mm to be exact.

From my scatter graph, I can see that there is SOME correlation between heights and hand spans of year seven girls.  This means that the taller the girl, the SOME the hand span. I can tell this because the best fit line on my scatter graph goes SOMEwards

If I had longer on my coursework, I would compare the heights of year 9 boys and girls, by using a box and whisker diagram, and simply comparing the means.

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