# Year 10 students generally over estimate obtuse angles but under estimate acute angles

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Introduction

Year 10 students generally over estimate obtuse angles but under estimate acute angles I took the sample for this, my third hypothesis, using stratifying. But it was a large stratifies compared to the just gender one in the last hypothesis. It was according to set. There were 187 pupils questioned in year 10, 92 of whom were male and 86 who were female. I decided to take 25 of each gender, and then the following numbers from each set: Male Female Higher (set 1) 28/92 x 25 = 7 24/86 x 25 = 7 Intermediate (sets2-3) 50/92 x 25 = 14 54/86 x 25 = 16 Foundation (set 5) 14/92 x 25 = 4 8/86 x 25 = 2 Total: 25 25 I then used my calculator on the random number generator setting to take the above numbers from each set and gender. Using the same formula I used in my second hypothesis I identified, removed and replaced my outliers. ...read more.

Middle

The fact that I had left many outliers which are 120 has to be taken into account as I took out the individual outliers which were much higher but the lower ones were in a big group. As both of the interquartile ranges on my box plots were equal and symmetrical I decided to look to see if there was any correlation between them. To do this I used Excel to generate a scatter diagram with each person in my sample's estimate of angle one plotted against their estimate of angle two. The scatter diagram can be seen on the next page, it does not show much correlation, but if any had to be seen it would be slightly negative as the people who underestimate on angle one appear to over estimate on angle two, but this could just be looking for a pattern which isn't there. This is why I then used excel to calculate the correlation co-efficient, which came out as: -0.012727, which shows that what I interpreted from my diagram is correct that there is very slight negative correlation. ...read more.

Conclusion

The cumulative frequency graph for angle one shows me that there is a higher gradient just above the actual value than below, whereas on the graph for angle two we see a steeper gradient directly below than directly above, although on the second graph, above the actual value carries on at a relatively steep gradient for a while where as below is a short steep gradient followed by a long small gradient. I have used the following methods to investigate and display the data to form a conclusion for or against my hypothesis: * Scatter diagram * Box plots * Cumulative frequency graphs These each told me the following things: * Scatter diagrams: People generally overestimate acute angles and underestimate obtuse angles * Box plots: People generally overestimate acute angles and underestimate obtuse angles * Cumulative frequency graphs: People generally overestimate both types of angles These finding are in general against the hypothesis that: Year 10 students generally over estimate obtuse angles but underestimate acute angles Proving that for our year 10 at Horsforth School, Leeds, my hypothesis is incorrect. Ellen Beardsworth - Maths Coursework - Guestimate ...read more.

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