Statistics 1 Revision Notes - Mr Barton Maths

More documents

Recommendations

Info

You must always remember the possibility of more than one order. In rolling four DICE, exactly TWO SIXES can occur in six ways: SSNN, SNSN, SNNS, NSSN, NSNS, NNSS, each of which would have the same probability = and so the probability of exactly two sixes with four dice is 6 × = . 7 Correlation Scatter diagrams Positive, negative, no correlation & line of best fit. no correlation positive correlation negative correlation The pattern of a scatter diagram shows linear correlation in a general manner. A line of best fit can be draw by eye, but only when the points nearly lie on a straight line. Product moment correlation coefficient, PMCC Formulae The are all similar to each other and make other formulae simpler to learn and use: S xy = = 1 S xx = = 1 S yy = = 1 The PMCC r = S S xx xy S yy , –1 ≤ r ≤ +1 for proof, see appendix To calculate the PMCC first calculate S xx , S yy and S xy using the second formula on each line. N.B. These formulae are all in the formula booklet. 28 14/04/2013 <strong>Statistics</strong> 1 SDB
Coding and the PMCC To see the effect of coding on the PMCC, it is better to use the first formula on each line. Example: Investigate the effect of the coding t = on the PMCC. Solution: r xy = ∑ ∑ ∑ t i = ⇒ x i = at i + k and = a + k ⇒ r xy = ∑ ∑ ∑ = ∑ ∑ ∑ = ∑ √ ∑ ∑ = ∑ ∑ ∑ = r ty In other words, the coding on x has had no effect on the PMCC. Similarly, coding on y has no effect on the PMCC. ⇒ Coding has no effect on the PMCC. 14/04/2013 <strong>Statistics</strong> 1 SDB 29
Page 1 and 2: Statistics 1 Revision Notes June 20
Page 3 and 4: 4 Median (Q 2 ), quartiles (Q 1 , Q
Page 5 and 6: 11 Context questions and answers 42
Page 7 and 8: 2 Representation of sample data Var
Page 9 and 10: Cumulative frequency curves for gro
Page 11 and 12: 3 Mode, mean (and median) Mode The
Page 13 and 14: 5 20 since 1 and Exa
Page 15 and 16: The interquartile range, I.Q.R., is
Page 17 and 18: ⇒ Q 1 = 4⋅5 + 5 × = 7⋅7421
Page 19 and 20: The same ideas apply for a continuo
Page 21 and 22: 1 2 1 Rough chec
Page 23 and 24: 6 Probability Relative frequency Af
Page 25 and 26: Tree diagrams The rules for tree di
Page 27: But ⇒ ⇒ P(A ∩ B) = P(A) × P(
Page 31 and 32: (c) r = - 0⋅725 is ‘quite close
Page 33 and 34: ⇒ b = = . . = 1⋅773584906
Page 35 and 36: Expectation algebra E[aX + b] =
Page 37 and 38: The expected variance, Var[X] = σ
Page 39 and 40: The general normal distribution N(
Page 41 and 42: Example: The weights of chocolate b
Page 43 and 44: Question 2 Statistical models can b
Page 45 and 46: Question 2 Give two other reasons w
Page 47 and 48: Question 5 Interpret the value of a
Page 49 and 50: 12 Appendix -1 ≤ P.M.C.C. ≤ 1 C
Page 51 and 52: Normal Distribution, Z = The stan

Statistics 1 Revision Notes - Mr Barton Maths

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?