After selecting my samples from each year group, I then looked at how many males and females I had randomly selected from each year. From year 7 I found I had selected 10 males and 11 females, making up the 21 that I worked out I needed to take from year 7. From year 8 I found I had selected 12 males and 8 females, making up the 20 that I worked out I needed to take from year 8. From year 9 I found I had selected 7 males and 12 females, making up the 19 that I worked out I needed to take from year 9. Next I created a scatter diagram for each year group to see any correlation between IQ and Amount of time spent watching T.V. and to compare males and females. In the year 7 diagram, I could see no obvious correlation between the 2 areas in either males or females. The average IQ for people in this year I could see to be between 94 and 103 and the average TV hours for people in this year I could see to be about 10 to 20 hours. In the year 8 diagram, I could also a slight correlation between the 2 areas showing slightly that in this case the lower the IQ the more hours of TV watched. The average IQ I estimate to be slightly higher than year 7, because in this case all of the students had an IQ of 94 or higher, unlike year 7. In the year 9 diagram, I could also see a slight correlation slightly proving my hypothesis. The data was widely spread, so I could not see a general average for either IQ or hours of TV from the diagram. To back up my scatter diagrams I also did Spearman’s Rank Correlation of the 3 year groups.
YEAR 7
∑ = 1109
Spearman’s Rank = 1 - 6∑d²
n(n²-1)
Spearman’s Rank = 1 - 6∑d²
21(21²-1)
Spearman’s Rank = 1 - 6∑d²
9240
Spearman’s Rank = 1 – 6630
9240
Spearman’s Rank = 1 – 0.718
Spearman’s Rank = 0.282. This shows a very weak correlation between the 2 areas, IQ and Average amount of time spent watching TV. This backs up my scatter diagram analysis but does not back up my original hypothesis.
YEAR 8
∑ = 1597
Spearman’s Rank = 1 - 6∑d²
n(n²-1)
Spearman’s Rank = 1 - 6∑d²
20(20²-1)
Spearman’s Rank = 1 - 6∑d²
7980
Spearman’s Rank = 1 – 9582
7980
Spearman’s Rank = 1 – 1.2
Spearman’s Rank = - 0.2. Similar to year 7, this also shows a very weak correlation between the two areas, IQ and amount of time spent watching TV. This also adds to my scatter diagram analysis, as this year 8 sample proves to have a higher correlation than the year 7 sample. This now adds to my hypothesis, as it proves there may be a possibility that the correlation between TV and IQ becomes greater as you get older.
YEAR 9
∑ = 1531
Spearman’s Rank = 1 - 6∑d²
n(n²-1)
Spearman’s Rank = 1 - 6∑d²
19(19²-1)
Spearman’s Rank = 1 - 6∑d²
6840
Spearman’s Rank = 1 – 9186
6840
Spearman’s Rank = 0.34. This shows a reasonable correlation between IQ and TV in year 9 pupils. This backs up my scatter diagram analysis and proves my hypothesis that the relationship between the 2 areas gets stronger as you move up the school.
For each set of information for years 7, 8 and 9 I then totalled all of the pieces of data and divided by the number of pieces to get the mean. All means are to 1 decimal place. I will now use the tables to perform standard deviation for each year group on Amount of time spent watching TV to find out how spread out the data is.
YEAR 7
YEAR 8
YEAR 9
I grouped the IQ into different categories for each year group to prepare for making a histogram to help prove my hypothesis.
YEAR 7
I chose to group the Males in year 7 starting with 72 because 72 was the lowest IQ value of the year 7 males. I then looked at the groups and at what the frequency would be if I used certain values, and changed and altered the groups until I created groups that would end up with generally the same frequency to make things easier. I chose to end to groups at 110 because the last year 7 Male value as 109 and so 109 would be included in that group. I did the same for both Males and Females for each year group.
YEAR 8
YEAR 9
I then drew Histograms of the values I found in the above totals which are included with this work. My analysis of them is below:
I firstly drew a histogram of frequency density comparing the IQs of year 7 boys and girls. From my histogram I could see that the girls’ data was more close together than the boys’ data. I could also see that in my sample the lowest girl’s IQ was higher than the lowest boy’s IQ and the same for the highest IQs. I can say from this histogram that in year 7 girls are generally more intelligent than boys.
Next I drew a histogram of frequency density comparing the IQs of year 8 boys and girls. From my histogram I could see that the girls’ data was again more close together but this time the boys had a generally higher than the girls. I can say from this histogram that in year 8 the boys are generally cleverer than girls but the range of boys’ intelligence is much more spread out.
My final histogram of frequency density was to compare the IQs of year 9 boys and girls. From my histogram I could see that once again the girls had a higher value for each the lowest IQ and the highest IQ out of the two sexes. From all of my histograms I can say that in year 7 girls are generally cleverer, but boys seem to catch up with intelligence in year 8, but girls become the most intelligent again by year 9. This is what my results tell me, but if I had used a bigger sample size I may have discovered something different.
I will now use the tables I created earlier to perform standard deviation for year 8 to see if my histogram was correct in showing year 8 boys to all be included in a smaller range of IQ which didn’t agree with my other 2 histrograms.
This standard deviation has shown me a value higher for year 8 males than year 8 females, disproving my analysis of my histogram for the sample I chose. (The higher the standard deviation the more spread out the data is). So, in all 3 year groups the data is more spread out and varied in males than in females.
In this investigation I have found out that in years 7, 8 and 9 the IQ is more spread out for males and that the females’ IQs are closer together. I have also found that there is no strong correlation in either of the 3 year groups between Amount of time spent watching TV and IQ. I have found that generally in years 7, 8 and 9 girls are more intelligent than boys. I disproved one of my hypotheses because I found that there was no great correlation between IQ and TV in any year group. I proved another of my hypotheses in that I found girls were generally more intelligent than boys throughout Key Stage 3. Overall, some of my hypotheses were proven in this investigation, and some were not – but they were all either proven or unproven by my statistical analysis.
