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• Level: GCSE
• Subject: Maths
• Word count: 4209

GCSE Statistics Coursework

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Introduction

Kevin Sharp

Statistics GCSE coursework

Kevin Sharp

In my DT lesson our teacher told us to draw a 25cm line and I drew mine too big and the teacher told me to get better at maths. I did not think this would improve my ability to estimate a length of a line so decided to find out. The questions I thought up are:

1) Is there any relationship between estimating a length of a straight line linked to mathematical ability?

Null hypothesis: There is a relationship between them.

Alternative hypothesis: There is no relationship between them.

2) Does the estimation of a non straight line improve after practice?

Null hypothesis: Practice improves the estimation of a non straight line.

Alternative hypothesis: Practice doesn’t improve the estimation of a non straight line.

3) Does a 14/15 year olds ability to estimate the length of a straight line fit a normal distribution?

Null hypothesis: A 14/15 year olds ability to estimate a straight line fits normal distribution.

Alternative hypothesis: A 14/15 year olds ability to estimate a straight line doesn’t fit normal distribution.

4) Are a 14/15 year olds ability to estimate a straight line more accurate than estimating a non straight line?

Null hypothesis: A 14/15 year olds ability to estimate a straight line is more accurate than estimating a non straight line.

Alternative hypothesis: A 14/15 year olds ability to estimate a straight line is less accurate than estimating a non straight line.

To get this data I am going to test 14/15 year olds in England as they have the same amount of education and experience. 14/15 year old can be used as a sample of England’s population to some degree of accuracy.

...read more.

Middle

Y on X Regression Line: y=-0.4009x+67.42

Line of best fit: y=-0.4009x+67.42.

Both the line of best fit and the y on x regression line have the same equation.

The 67.42 shows where the line crosses the exam mark axis and the -0.4 gives the gradient of the line.

Substituting x = 43 in to the equation =-0.4009x+67.42, y = 50.1813

So if a pupil estimated the line with a difference of 43 from the actual length, a rough estimate of what his exam result might be is 50%.

If you wanted to roughly estimate an estimate difference of a straight line from someone who got 59% in the year 9 end of year exam you could find out by using an x  dependant on y regression line.

This scatter graph shows the x  dependant on y regression line.

x-on-y regression Line: x=-0.3949y+50.02

If someone got 59% in his exam then he may have estimated the straight line with a difference of about 27mm.

However these results are not very accurate as there is not a very strong correlation.

These results are related to my sample investigation. For the reasons stated at the beginning of my project I think that these results will relate both to the study population and the target population. However within these populations more variations of these results could be expected.

2) Does the estimation of a non straight line improve after practice?

Null hypothesis: Practice improves the estimation of a non straight line.

Alternative hypothesis: Practice doesn’t improve the estimation of a non straight line.

Sample:

I got 86 results for boys and 52 results for girls.

...read more.

Conclusion

Here is another histogram but showing the results between the 2nd +/- standard deviations:

Between the 2nd +/- standard deviations (-76 and 80) there is 93% of results. This is very close to 95% and shows a very strong similarity between the results and a normal distribution. As you can see, 100% of results are between the 3rd standard deviations and shows strong similarities between the results and a normal distribution.

My results are very close to a normal distribution showed by the amount of results between +/- 3 standard deviations and proves strongly my null hypothesis.

4) Are a 14/15 year olds ability to estimate a straight line more accurate than estimating a non straight line?

Null hypothesis: A 14/15 year olds ability to estimate a straight line is more accurate than estimating a non straight line.

Alternative hypothesis: A 14/15 year olds ability to estimate a straight line is less accurate than estimating a non straight line.

The sample used will be the same as used in question 2 and 3. The data I will use the distance from actual of a straight line and distance from actual of a non straight line before practise (before practise because the pupils did not have practise before estimating the straight line).

Here is the data I will use copied from excel:

 St line length Diff from 234 Non st.line length Diff from 351 152 -82 185 -166 195 -39 238 -113 172 -62 172 -179 263 29 263 88 172 -62 172 179 189 -45 189 -162 320 86 290 -61 245 11 500 149 240 6 280 -71 250 16 340 -11 265 31 285 66 256 22 262 -89 210 -24 280 -71 258 24 308 43 210 -24 280 71 257 23 315 36 284 50 249 102 250 16 300 -51 200 -34 400 49 150 -84 480 129 250 16 180 171 226 -8 219 132 250 16 250 -101 270 36 270 81 200 -34 200 -151 250 16 250 -101 228 -6 314 37 181 -53 221 130 180 -54 245 -106 270 36 270 -81 232 -2 297 54 257 23 314 37 211 -23 300 51 200 -34 305 -46 230 -4 200 -151 274 40 424 -73 250 16 300 -51 240 6 310 41 200 -34 303 -48 255 21 355 -4 203 -31 450 -99 225 -9 225 -126 250 16 300 -51 282 48 357 6 186 -48 197 154 250 16 200 -151 240 6 210 -141 248 14 250 -101 175 -59 300 -51 240 6 310 -41 276 42 322 -29 270 36 350 -1 243 9 348 3 250 16 300 51 235 1 250 101 289 55 350 -1 182 -52 325 26 267 33 309 42 243 9 342 9 323 89 325 -26 241 7 363 -12 230 -4 410 59 245 11 315 36 232 -2 283 68 250 16 370 -19 137 -97 323 -28 176 -58 368 -17 240 6 230 -121 250 16 290 -61 250 16 370 19 274 40 349 2 209 -25 302 49 282 48 392 -41 285 51 428 -77 300 66 300 -51 210 -24 400 -49 300 66 400 -49 250 16 500 149 242 8 421 -70 270 36 411 -60 317 83 453 -102 268 34 244 107 272 38 433 -82 256 22 427 -76 200 -34 200 -151 217 -17 242 109 195 -39 152 -199 150 -84 200 -151 250 16 250 -101 200 -34 230 -121

...read more.

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