# AQA STATISTICS 1 REVISION NOTES

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2 PROBABILITY Outcome : each thig that ca happe i a experimet Sample Space : list of all the possible values q NOTATION A Ç B A ad B both happe A È B either A or B or both happe C' C does t happe C P(C ) = 1 P(C) P(A È B) = P(A) + P(B) P(A Ç B) Mutually Exclusive Evets two or more evets that caot happe at the same time P(A È B) = P(A) + P(B) Idepedet Evets the outcome of oe evet does ot affect the outcome of aother P( B ) = P(A) P(B) A Ç Coditioal Probability : whe the outcome of the first evet affects the outcome of a secod evet, the probability of the secod evet depeds o what has happeed P(B/A) meas the coditioal probability of B give A P(B/A) = P(A Ç B) P(A) A Ç so P( B )= P(A) P(B/A) q If the questio states that the evets are idepedet the a tree diagram might be a good idea multiply alog the braches the add the appropriate combiatios together q Probability of at least 1 = 1 Probability of oe q If you are asked to fid probabilities usig data i a table work out the row/colum totals before you start

7 q SCALING either the x or the y values will chage the equatio e.g y = x If the x values are doubled the the equatio becomes y = (2x) y = x CORRELATION If 5 is added o to each of the y values the the equatio becomes y + 5 = x y = x (always rearrage to get y = a + b x) The Product Momet Correlatio Coefficiet : is a umerical measures of the stregth ad type of correlatio deoted by r ad will lie i the rage -1 r 1 q idicates how well the data, whe plotted i a scatter graph, fits a straight lie patter q NOT APPROPRIATE if the data does ot follow a liear patter whe plotted (straight lie) so scatter graph is eeded to check this q If you are give a table of values use your calculator to fid r (If you have time it s a good idea to check that you have etered your values correctly) q If you are calculatig usig summary values -make sure you use the formula book showig how you substituted the values ito the formula INTERPRETING r make sure you do this i the cotext of the questio (ot just positive correlatio) e.g. There appears to be a fairly strog relatioship betwee temperature ad ice cream sales, higher temperatures appear to correspod to higher values of ice-cream sales ad vice versa. q Scalig data a liear trasformatio or scalig of oe or both of the variables will ot affect the correlatio coefficiet all of the poits will stay i the same positio RELATIVE to each other TAKE CARE q Not all correlatio will be liear For this data, the correlatio coefficiet is close to 0 This does ot mea that there is o correlatio but simply mea that there is o liear correlatio (patter appears to be quadratic) q Spurious Correlatio A strog correlatio betwee 2 variables does ot mea that oe thig causes the other high marks i a maths exam do ot ecessarily cause high marks i a Statistics exam, they are likely to both be depedet o a commo third variable : the studets mathematical ability q Outliers Oe or two outliers ca have a dramatic effect o a correlatio coefficiet

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