Statistics 1 Revision Notes - Mr Barton Maths

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Solution: Lower boundary for outliers is 12 – 1⋅5 × (17 – 12) = 4⋅5 Upper boundary for outliers is 17 + 1⋅5 × (17 – 12) = 24⋅5 ⇒ 3 and 26 are the only outliers. To draw a box plot, put crosses at 3 and 26, and draw the lines to 6 (the lowest value which is not an outlier), and to 21 (the highest value which is not an outlier). lowest value not outlier Q 1 Q 2 highest value not outlier × × Q 3 5 10 15 20 25 age Note that there are other ways of drawing box plots with outliers, but this is the safest and will never be wrong – so why not use it. Skewness A distribution which is symmetrical is not skewed Positive skew If a symmetrical box plot is stretched in the direction of the positive x-axis, then the resulting distribution has positive skew. Q 1 Q 2 Q 3 PULL Q 1 Q 2 Q 3 For positive skew the diagram shows that Q 3 – Q 2 > Q 2 – Q 1 18 14/04/2013 <strong>Statistics</strong> 1 SDB
The same ideas apply for a continuous distribution, and a little bit of thought should show that for positive skew mean > median > mode. PULL mode mean median Negative skew If a symmetrical box plot is stretched in the direction of the negative x-axis, then the resulting distribution has negative skew. Q 1 Q 2 Q 3 PULL Q 1 Q 2 Q 3 For negative skew the diagram shows that Q 3 – Q 2 < Q 2 – Q 1 The same ideas apply for a continuous distribution, and a little bit of thought should show that for negative skew mean < median < mode. PULL 14/04/2013 <strong>Statistics</strong> 1 SDB 19
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: ⇒ Q 1 = 4⋅5 + 5 × = 7⋅7421
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 and 28: But ⇒ ⇒ P(A ∩ B) = P(A) × P(
Page 29 and 30: Coding and the PMCC To see the effe
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

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