Upper Quartile = 24 / 4 * 3 = 18 106.0
Inter-Quartile Range = 106.0 – 100.0 = 6
Box and Whisker Diagrams
Standard Deviation
This shows the average difference of numbers from the mean. The Standard deviation is the average distance a number is from the mean of all the numbers. Standard Deviation is more reliable than range because it uses all results to make a range not just the highest and lowest.
Male = 10.733
Female = 6.998
Average Test Score
Male
Lower Quartile = 26 / 4 = 6.5 3.33
Median = 26 / 2 = 13 4.33
Upper Quartile = 26 / 4 * 3 = 19.5 4.50
Inter-Quartile Range = 4.50 – 3.33 = 1.17
Female
Lower Quartile = 24 / 4 = 6 3.67
Median = 24 / 2 = 12 4.00
Upper Quartile = 24 / 4 * 3 = 18 4.33
Inter-Quartile Range = 4.33 – 3.67 = 0.66
Box and Whisker Diagrams
Standard Deviation
This shows the average difference of numbers from the mean. The Standard deviation is the average distance a number is from the mean of all the numbers. Standard Deviation is more reliable than range because it uses all results to make a range not just the highest and lowest.
Male = 0.817
Female = 0.564
IQ
The Box and whisker diagrams show that men have a larger spread of IQ than women. The Median is in the same place but the Interquartile range, 50% of the sample is much wider than the women’s which shows that half the men have a larger range that half the women. While the man’s upper range is very similar to that of the woman’s the man’s lower range is much lower than the women’s lower range. Both the man’s range and the Inter-Quartile range are much larger than the women’s.
The Standard Deviation of men is larger than that of the women’s, by nearly 4. This shows that the spread of IQ is much wider.
The Histogram of results for men is much more widely spread than that of the one for women showing that the men have a wider range of IQ.
Average Test Score
The Box and Whisker Diagram show that men have a much larger Inter-Quartile range than women this means that 50% of the men have a larger range than 50% of the women, the median of the men is close to the Upper quartile of the women meaning 50% of men are above 75% of women. While the Inter-Quartile range of the men is larger than the women’s the range is more or less the same size, the man’s highest one is approximately 2/3 lower than the women’s and the lower range is approximately 2/3 lower than the women’s.
The Standard Deviation of the men is approximately 1 and 1/2 larger than that of the women’s. This shows a larger range of Test Scores
The Histogram of results for men is much more widely spread than that of the one for women showing that the men have a wider range of Average Test Score. If drawn like a pyramid the women’s would be a much more steeply sloped one.
My Hypothesis was correct and I found that I could get the results for it quite easily. I had no problems in obtaining my sample other than at times it could be quite tedious. I found it easy to write the stem and leaf diagrams, and the box and whisker diagrams gave me no trouble to draw. The main troubles came when entering data into my calculator and this was extremely tedious, I had to enter information for standard deviation and regression, both of which I had to restart because of mistakes and had to repeat to check. This took up a lot of my time, which was annoying.
Hypothesis:
My second hypothesis is that people with high IQ’s have high Average Test Scores and vice-a-versa.
Test The Hypothesis:
I believe this because IQ is supposed to be a test of intelligence and intelligent people should get higher scores.
My Hypothesis means that I am not required to take any more samples as the data is already available this is useful as taking sample’s is a tedious process but I will be required to reduce my sample to 48 to remove 2 male samples as gender should not be allowed to bias my results in any way, to choose the two I will remove my sample size is 24 out of. I have 24men to sample I will use my calculators Random number button then multiply it by 26 I will repeat once for 2 results. If I get a number twice I will redo it. Press the shift button the press Rnd with Rnd# above it then press * and 2 6.
15 and 23 are to be removed from my sample.
Box And Whisker Diagrams
Regression
This is a function on my calculator that allows me to find out how well the correlation of a graph is, 1 is exact positive correlation, -1 is exact negative correlation and 0 is no correlation. This graph has 0.8297 correlation. The Scatter graph shows that there is positive correlation between IQ and Average Test Score.
Press Mode then Reg3 then Lin1 then press shift and then AC with Scl above it. Now enter each pair of co-ordinates X X X , X X X then press M+. Then press shift and then ( with r above it.
This graph has a very good correlation as it shows strong positive correlation, linking high IQs with high Test Scores. The graph’s correlation shows that my Hypothesis was correct and a high IQ indicates high Test Scores. The box and whisker diagrams are roughly the same size and shape that shows that IQ and Test Scores are related.