# 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.

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.

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 |

This student written piece of work is one of many that can be found in our GCSE IQ Correlation section.

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