# 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:MaleFemaleHigher (set 1)28/92 x 25 =724/86 x 25 =7Intermediate (sets2-3)50/92 x 25 =1454/86 x 25 =16Foundation (set 5)14/92 x 25 =48/86 x 25 =2Total: 25 25I 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. But I did find that although the lower boundary for angle 2 was 141.

5 many people in this sample estimated it at 120 which suggested to me that it must have been quite typical so I left these values in. Over the whole sample I replaced 7 lots of information.I then placed the information into a spreadsheet such as the one shown on page ?. This made it easy for me to compare, enter formulas and produce graphs based on the data. My first step in investigating this data was to produce box plots to see if the inter-quartile range was largely above or below the median, which will tell me whether the data was positively or negatively skewed for each angle.

These two box plots at first look did not really help prove my hypothesis either way, but then I drew on each box the actual value of the angles they were trying to estimate. This showed me that on angle one although the spread of data was symmetrical, it was all above the actual value as the value was equal to the lower quartile. This shows the opposite to my hypothesis that people overestimate actuate angles, not underestimate.The second box plot shows me that although the quartile range was symmetrical and directly over the actual value with the median being equal to it, the whiskers aren’t and the longer one shows guesses lower than the actual value, showing people underestimating obtuse angles more than overestimating them. Again working against my hypothesis.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.When I look at the graph I see that there are a greater concentration of points on the right hand side which suggests people overestimate angle one, which again is against my hypothesis.

The final way for me to investigate whether people did really overestimate obtuse angles and underestimate acute angles was to look at the data on a cumulative frequency graph and discover whether people were more probable to be within 10% above or below each actual value.Below are the tables that I used to accumulate the data:Size (*)FrequencyCumulative Freq.40(a;451145(a;504550(a;5561155(a;60102160(a;65153665(a;7033970(a;7584775(a;80350Size (*)FrequencyCumulative Freq.120(a;12533125(a;13003130(a;13525135(a;14016140(a;14539145(a;15009150(a;1551524155(a;160731160(a;1651445165(a;170449170(a;175150The graphs can be seen on the next page, the results found from the graphs are in the table below:BelowAbovePeople within 10%ProbabilityPeople within 10%ProbabilityAngle one612%1122%Angle two1836%2448%This tells me that people are more likely to be above both graphs with their estimates. But this is only the people within 10% of the actual value, all the rest of the guesses could be below, therefore I will look at the shape of the graphs.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 graphsThese 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 anglesThese finding are in general against the hypothesis that:Year 10 students generally over estimate obtuse angles but underestimate acute anglesProving that for our year 10 at Horsforth School, Leeds, my hypothesis is incorrect.Ellen Beardsworth – Maths Coursework – Guestimate