Women 32 ÷ 81 × 30 = 12
I randomly chose 18 men and 12 women from the list using the Ran# function on the calculator.
Ran# × 81 then press =
Random Results tables
Women
Men
Averages
The mean average is found by adding up all the numbers then dividing this by how many numbers there are.
The median is the middle number when all numbers are in numerical order.
The mode is the most common number; the number which appears the most.
The range is the largest number minus the smallest number.
Average results
Men – Lines
Results in numerical order are:
2.5, 2.5, 4, 4, 4, 4, 4, 4.3, 4.5, 4.9, 5, 5, 5, 5, 7, 7, 12, 12
Mean is 96.7 ÷ 18 = 5.34cm
Median is 4.7cm
Mode is 4cm
Range is 9.5cm
Men – Angles
Results in numerical order are:
30, 32, 40, 40, 43, 45, 45, 45, 45, 45, 45, 45, 45, 45, 60, 60, 90, 90
Mean is 880 ÷ 18 = 49°
Median is 45°
Mode is 45°
Range is 60°
Women – Line
Results in numerical order are:
4, 4, 4, 4, 4.5, 5, 5, 5, 5, 5, 5, 5
Mean is 59.5 ÷ 12 = 4.9cm
Median is 5cm
Mode is 5cm
Range is 1cm
Women – Angles
Results in numerical order are:
25, 35, 40, 40, 45, 45, 45, 45, 45, 45, 45, 45
Mean is 500 ÷ 12 = 42°
Median is 45°
Mode is 45°
Range is 20°
Averages Tables
Lines cm
As the actual length of the line is 4.5cm the women’s results are more accurate than the men’s for the mean as the women’s are only 0.4cm out whereas the men’s are 0.9cm out.
The median results show that the men’s result was 0.2cm out while the women’s were 0.5cm out.
The mode result shows that they were both 0.5cm out so they were as accurate as each other. The range shows that the difference is 9.5cm for men yet only 1cm for women, making the women’s result more accurate.
Overall these results show that if you looked at the averages then men and women were as good as each other at guessing the length of the line but the range is much greater for men than women, this could be due to just a couple of men having poor, inaccurate guesstimates. I will investigate this further by doing frequency polygons
Angles °
As the actual size of the angle is 38° the women’s results are more accurate than the men’s for the mean as the women’s were only 4° out while the men’s were 11° out.
The median results show they are both 7° out so they were both as accurate as each other.
The mode results show that they are both 7° out so again they were as accurate as each other.
The range results show that the difference is 60° for men and 20° for women, making the women’s results more accurate.
Overall these results show that if you looked at the averages women were better at guesstimating the size of an angle; although both men and women were as accurate as each other for the median and the mode the women were much more accurate than the men for the mean. The median and the mode were not affected by the high guessitmates. The range for men is much greater than the range for women; this could be due to just a couple of men making poor guesstimates. I will investigate this further using frequency polygons.
Frequency tables
Men- Lines
Women –Lines
Men – Angles
Women –Angles
Analysis Of Frequency polygons
The frequency polygon for the line estimates show that women guesstimated more accurately than men. Four women underestimated while seven men underestimated. Seven men guessed correctly while eight women guessed correctly. Four men overestimated while no women overestimated. This shows that although most of the men guessed correctly, as did most women, the men’s range is much greater due to just four anomalous overestimations.
22.2% of men overestimated, almost a quarter.
38.9% of men guessed correctly.
38.9% of men underestimated.
33.3% of women underestimated.
66.7% of women guessed correctly.
The frequency polygon for the angle estimates show that two women underestimated and two men underestimated. Two women guessed correctly and two men guessed correctly. Eight women overestimated and fourteen men overestimated.
66.7% of women overestimated
16.7% of women guessed correctly.
16.7% of women underestimated
77.8% of men overestimated.
11.1% of men guessed correctly.
11.1% of men underestimated.
Although the percentage of men and women who overestimated are both quite high, women is two thirds and men is over three quarters, the men’s range is much bigger due to two estimations being ridiculously large. The percentages can be seen more clearly in the pie charts below.
Box Plot Analysis
By doing the cumulative frequencies and then the box plots we are able to look at the interquartile range, this is a measure of statistical dispersion that is more stable than the range.
Lines
The box plots showed us that the women’s answers were in a tight area while the men’s answers were more dispersed. The women’s results skewed towards smaller answers and the men’s results were both over and under the actual length of the line.
75% of men in the interquartile range underestimated and 25% overestimated.
100% of women in the interquartile range underestimated.
Although three quarters of men in the interquartile range underestimated all the women did.
Angles
The box plots showed us that all men overestimated while the women’s results were quite evenly dispersed between overestimations and underestimations. The men’s interquartile range was in a much tighter area then the women’s showing that the middle 50% of guesses were closer together.
100% of men in the interquartile range overestimated.
25% of women in the interquartile range underestimated.
75% of women in the interquartile range overestimated.
Standard Deviation.
This is a measure of spread from the mean.
Men – Lines
Divide the result by the number of guesses then find the square root on the calculator.
126.5 ÷ 18 = 7.03
Square root (50.14) = 2.65
Women – Lines
3.47 ÷ 12 = 0.29
Square root (0.29) = 0.54cm
These standard deviations show that that the women’s are much smaller than the men’s, this was due to the mean average being much closer for the women than the men.
Men –Angles
4476 ÷ 18 = 248.66
Square root (248.66) = 15.77
Women –Angles
178 ÷ 12 = 14.83
Square root (14.83) = 3.85
These results show that the women’s are again much lower than the men’s results.
Conclusion
To conclude this investigation I will refer back to my original hypothesis where I stated that I thought men would be much better at guesstimating the length of a line and the size of an angle. Throughout this investigation my hypothesis has been proven to be wrong. The women’s guesses for the lines were all very close to the actual length whereas the men’s guesses, although 66.6% were as close to the actual length as the women’s, due to either much larger or smaller guesstimates ended up having a much larger range. This investigation has shown that men are more likely to overestimate, while women although fairly reliable are more likely to underestimate.
The angle estimates showed similar findings to the line estimates. Men are not as reliable as women when guessing the size of an angle. The men tended to overestimate their guesses and some of the results were ridiculously high.
Overall the results of this investigation have shown that women are more likely to be able to guess the length of a line and the size of an angle than men.
Evaluation
This experiment was a fair experiment as I used random sampling and a stratified sample to collect my results.
Cumulative frequencies were used to obtain the results from the interquartile range and how dispersed the guestimates were.
Standard deviations were used to show the results more clearly.