Statistics 1 Revision Notes - Mr Barton Maths

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Contents 1 Statistical modelling 6 Statistical modelling ............................................................................................................ 6 Definition ........................................................................................................................................................ 6 Advantages ..................................................................................................................................................... 6 Disadvantages ................................................................................................................................................. 6 2 Representation of sample data 7 Variables ............................................................................................................................. 7 Qualitative variables....................................................................................................................................... 7 Quantitative variables .................................................................................................................................... 7 Continuous variables ...................................................................................................................................... 7 Discrete variables ........................................................................................................................................... 7 Frequency distributions ....................................................................................................... 7 Frequency tables ............................................................................................................................................. 7 Cumulative frequency .................................................................................................................................... 7 Stem and leaf & back-to-back stem and leaf diagrams ....................................................... 8 Comparing two distributions from a back to back stem and leaf diagram. .................................................. 8 Grouped frequency distributions ......................................................................................... 8 Class boundaries and widths .......................................................................................................................... 8 Cumulative frequency curves for grouped data .................................................................. 9 Histograms .......................................................................................................................... 9 3 Mode, mean (and median) 11 Mode ................................................................................................................................. 11 Mean ................................................................................................................................. 11 Coding ............................................................................................................................... 12 Coding and calculating the mean ................................................................................................................. 12 Median .............................................................................................................................. 13 When to use mode, median and mean .............................................................................. 13 Mode ............................................................................................................................................................. 13 Median .......................................................................................................................................................... 13 Mean ............................................................................................................................................................. 13 2 14/04/2013 <strong>Statistics</strong> 1 SDB
4 Median (Q 2 ), quartiles (Q 1 , Q 3 ) and percentiles 14 Discrete lists and discrete frequency tables ...................................................................... 14 Interquartile range ........................................................................................................................................ 14 Discrete lists ................................................................................................................................................. 14 Discrete frequency tables ............................................................................................................................. 14 Grouped frequency tables, continuous and discrete data .................................................. 15 Grouped frequency tables, continuous data ................................................................................................. 15 Grouped frequency tables, discrete data ...................................................................................................... 16 Percentiles ..................................................................................................................................................... 17 Box Plots ........................................................................................................................... 17 Outliers ............................................................................................................................. 17 Skewness ........................................................................................................................... 18 Positive skew ................................................................................................................................................ 18 Negative skew .............................................................................................................................................. 19 5 Measures of spread 20 Range & interquartile range .............................................................................................. 20 Range ............................................................................................................................................................ 20 Interquartile range ........................................................................................................................................ 20 Variance and standard deviation ....................................................................................... 20 Proof of the alternative formula for variance .............................................................................................. 20 Rough checks, m ± s, m ± 2s ..................................................................................................................... 21 Coding and variance ..................................................................................................................................... 21 6 Probability 23 Relative frequency ............................................................................................................ 23 Sample spaces, events and equally likely outcomes ......................................................... 23 Probability rules and Venn diagrams ................................................................................ 23 Diagrams for two dice etc. ................................................................................................ 24 Tree diagrams ................................................................................................................... 25 Independent events ........................................................................................................... 26 To prove that A and B are independent ..................................................................................................... 26 Exclusive events ............................................................................................................... 27 Number of arrangements .................................................................................................. 27 14/04/2013 <strong>Statistics</strong> 1 SDB 3
Page 1: Statistics 1 Revision Notes June 20
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 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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