GCSE statistics- content summary

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ge decreases Cousel Relationship-When a change in svonable directly causes a change in another variable Correlation does not necessarily imply castin. En real life. situations, multiple factors interact focuse variables to change Line of Best Fit (LOBF) To get a good fit, drae your fire through the mean point (xy). Interpolation using your LOB to estinate within the range of values oireacy plattes. Usually reliable Extrapolation-Extending LOSF and reading des outside of the range of rches pieted Less reinible, Equation of LOBP: a gradient, o y-intercept correlation Cal SRCC/PMCC sacceasures the strength of the correlation between two variables SRCC & ALWAYS between-I and 1 ds diff between ranks Collecting Deta Questiomare a set of one designed to obton data ton Features sf a good questionare short questions, simple unquage no leading cuestione, nonovepping has, ts frane option tax ore exhaustive personal questions Open question has ne suggested •Cosed to host of given anawers to cheese from Plet survey was version of the survey to test the design and ads of that survey M If there is strong X=0ffers ne correlation IFP-2 hare u strong ve correlation SUCC 151 SRCC is best used for date that can be ranked and data that is non-linear PMCC-Tests for linear correlation Co extend arves before it is used where trof get regle Extraneus variables-woriables you are not interested in but could affect the rest of your experiment Central group used to test the effectiveness of a treatment Userundan selection to select 2 groups of people Give the test group the t Compare reads fromment control group to treatment growshow affective treatment Matched Pars Test-2 groups of equally matched (op/genderetc) prople used to test effect of a particular factor Everything in common except factor being studed. Sitions-model runden real life events to help you predict what could actually hoppes May be easier and cheaper than collecting realife dota Interview Queimar Interviewer con explain eveations Interviewer con pur people at when having te ver •Outliers Recent wwvers gh respones rate Dependente marely fo aver per Estond o lenge mple are Quik Chap Bangt- Largest Valus malest value Latera ronge 11091 Shewness FORUQ-LQ GCSE STATISTICS Measures of Dispersion/Spread <LQ (15*1QR) and UQ- (15 1QR) Grouped Data us Dieter Les hely tooner per questions and may be less h Salar mple sise than Interviewers interver atergrat arors to at ther dent may try t press the the Petersen Capture-Recapture Formula M N she population Myth the Love Quark (LG(+11+Have (dscor lethalefcunt) Cypce Quartile Network) er thun (chart) Interpercentile Range-difference between 2 percentiles Interdecile range difference between two deciles OR Some may be underst DD Rechers may not understand of the repre Low pr Standard Deviatich-A measure of how for all the volues are from the nean velue, or how spread out they are. Discrete. OR - Snowman) - Positive Skea Maanmadan mode Negative Skew Mean median mode may m 21 of of the the off the Assumptions Papuri honet denged-br/th Pritory of being caught wusity ay ter as divas Sample was lange nich First Capture Tolul (5) OR Mn N=- on Samping Tagged Second Captare Opportaity Sping 1 Deary'un chance of th The provided ter and the grand of nel to the the DESAKURuscondi Pondon Pesponse Method Uses a random event to decide kow to answer a question Find total who answered questions Find prob (heads) if it is a coin Estimate no, ef heads-Prob x total Estimate number of yes" answers that were truthful Yes unswer-estimated no of heads Estimate proportion of people who did the crime DIC Measures of Central Tendency/Averages Carryle Mode- most common value Modal Class class with the highest frequency Median Discrete data (n-1)th value Continuous data (with inequalities) - Inth value To estimate median from grouped data: Mean (x) Discrete data-x- Find cumulative frequency of freq column until you get to inth value and find the class interval with the median. See how many more values you need in that class to get the median Divide this number by the freq for that class. Multiply your answer by the class width Add your answer to the lower bound for the class interval. Estimated median-L+ a where L is the lower boundary of the class containing the median is the total number of values - Fis the cumulative frequency of the intervals before the one containing the medias Continuous data-x- is the frequency of the median class interval wis the width of the median class interval I. n = number of values 2x sum of all values - f = frequency x= first calumn (use k midpoints for grouped data) Weighted Mear-for data that has different number of values or weights for each group. Weighted Meanweight) wwights Geometric Mean Valueix value 2 xx valuen L can be wund with and qual, unEve butu 341 has the p ht Lakew b Maybede or care than one mode Cow beed to calculats maxres of spredd May net be a dete v affected by extreme wales Ce dorted typenied cara Aapning Ceta Sets SOC averags (mean meta/mude), potongs, ICK standard deszcr) or skenmess fra Toidual values and mention which t SU TUHmultor which one doarty Dagy pan come back to CORRE Smilte 96125Sorger Phot EN THE DATA n veican 45 for det's A tergestionat e saty Cup the Sextant Tape Sale/State & A were constant 2 soverlues are cleast to mod 40 for actress majority of t Box plat for data 4 megativacy shemed so majplayed hearts were high with few lor este Time Series A line graph with fime plotted on the x axis. Trend line shows the general trend of the date-ignone fluctuations and just follow the general pattern. Place the line roughly halfway betweenhighest and lowest point for each year. Trend line may show rising (upwards), folling (downward) or level trend. Seasonal variations-variations in a time series following a regular time period, like days of the week or seasons. Think about real life scenarios that may cause these Moving Averages-An average worked out for a given umber of successive observations. They smooth out luctuations in the data and make the trend line more.. sccurate Pat them at the midpoint of the time interval ond do not join them upuse a LOBF. Seasonal Variation Actual Value - Trend Value Estimated mean SV (EMSV) = Mean of all the SV for that season (eg. average of all quarter 4 SVs.), Also called average seasonal effect. Predicted Value Trend line value - EMSV Reliability of prediction depends on how far into the future prediction is made (further = less reliable) and how good the EMSV as trends and variations can unexpectedly change. Probability Prob. of an Event, P(event) m Number of successful outconer Total number of possible outcomes Outcome something that can happen as a result of a trial e g. heads or tails when flipping a coin Expected Frequency- The number of times you expect the event to happen, not necessarily what will happen • Expected Frequency= Ploutcome) x number of trials Estimated Probability of tricis with ful tema total number of trials As the number of trials increase the estimate for the probability gets close to the true value. Estimated prob is also called relative frequency. Risk-probability of cn event occurring for negative events No of trials in which event happens Risk of event- tetel no of trials Absolute Risk - how likely an event is to happen. Pelative risk- how much more likely an event is to happen for one group compared to evothar group. Relative Risk Rk for those in the group Risk for those not in greap Mutually Exclusive - CANNOT happen at same time Exhaustive The set contains ALL the possible outcomes For a set of mutually exclusive and exhaustive events the sum of probabilities is equal to 1. Addition Law for MF. events: • C. P(A or B) = P(A) P(B) P(A) P(not A) = 1 P(not A) = 1-P(A) General Add tion Low (for non-M.E. events-can occur together) *P(A or B)=P(A) - P(B)- P(A and B) PAP(A and B). On a Venn diagram this is the intersection or middle/overlapping part. PA or B). On a Venin dicgram this is the union of A and B and includes everything in both circles. Independent Events unconnected events. The outcome of one event does not affect the outcome of the other event. For two independent events, A and B: P(A and B)-F(A)*P(B). For 3 independent events, P(A and B and C;-P)4) X P(B) X P(C) P(at least 1):1-F(none) Conditional Probability-opposite of independent events, when an event affects another, P(BIA): P(B given that happens). The event that happened first comes lost in the bracket. How to know its conditional probability? Phrases like given that,for tells you about ons group and asks you to work out the prob of second event from that this group P(BIA): PA and B)= P(BIA) x P(A) Fand Pun For two independent events A and P(A)=P(AIB). You can use this formula to test if two events are independent. If P(A) and P(AIB) are not equal, the events are not independent and are instead conditional GCSE STATISTICS Revision Notes Ms Patel Probability Distributions A list of all the possible outcomes together with their probabilities Binomial Distribution p na of trials, p probability of success. Conditions (ase these to explain if binomial dist. is a suitable model) Fixed number of tricks (n) Each trial has two outtomes (success (p/failure(4) Eg on a dice, 6 or rot 6. All the trials are independent of each other, 4 Probability of success is constant (stays the same for each trial) Use (p-gi" to tind probabilities 1 2 3 4 Meen of Binomial Distribation B(np) is np You can find coefficients of binomial expansion on calculator using nor burton (on top of-) forn triale and r successes. 1. 2 3. Identify the 2 autcomes and find their probabilities 1. 2 3. Expend to To find pres of where n is number of tricks. Leave p and q es lerrers for now. sitcesses, find the term that has p to the power of x successes Substitute values of g and q into that ferm and calculate. Normal Distribution Nua) nean, ² variance Smeath bell shaped curve. Conditions The data is continuous (heights, weights time) The distribution is symmetrical Mode, median and mean are approximately qual Not suitable for skewed data 68% of data lie within 1 SD of the mean 95% of date lies with 2 50 of the mean 99.8% of data lies within 3 SD of the meani Standardised Scores used to compare how far chew bobeles re se inreldal values are Standardised Score smlard Dewation •scuremen acore neon Quality Assurance-Involves checieng sample to make sure products are of some quality. Control Chart-time series chart used for quality assurance. They have 5 lines: Torget value (middle line) -Upper and lower Warning Limits (inner two lines) -2 SD above/below target value. If somple is above warning line, another sample is taken to see if there is a problem and if so production stopped Upper und lower Action Limits (cuter two lines) - 3 5D chove/below target value. If sample outside ection limit production stopped smediately. Index Numbers Carports the price change of on item with its base year price Iso Troker Nipaber Ieder ber 100 Indo inser 100 100 your price increase in value decrease in velue. keroit Price Index (RPI)-Shows rate of change (inflationideflation) of prices of everyday goods such as mortgage, food and heating Consumer Price Index (CPI)-afficial measure of inflution csed by UK government. Similar to RPI but does not include mortgage payments. Grass Domestic Product (GDP) - Value of goods and services prediced in a county in a given amount of Time + GDP fails for 2 or more quarters, economy is in recession. Weighted Index Number-take into account proportions (similar to weighted meen). Weightings reflect mportance of different itens. Weighted index number= Chon Base index Numbers-compare prices from each year with previous year Chain fase IN RPI/CPI are chain base that show unnual or monthly % changes x 100 ist your price inferunbergh!! Levigtes de thcs-Number of births per thousand option Crude Sink Bard-number of deaths per tesudend of typoplation Cote de 10 Stundu Population-hypotharios pop of 100 pled to represent whole papoleti Storagiriation to Stundides allows you to singure son group in different options Stunt and our fustard puputall ww L