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# Further5 normal distribution

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### Further5 normal distribution

1. 1. Further MathematicsNormal Distribution K McMullen 2012
2. 2. Normal DistributionsPlease note that you need the correspondinggraphs to understand what is written in thepowerpointAlso, the standard score equation has not beengiven in the last slide K McMullen 2012
3. 3. Normal DistributionThe normal distribution is used when the data setis roughly symmetricalIn normal distributions, the percentage ofobservations that lie within a certain number ofstandard deviations of the mean can always bedetermined.Generally, we focus on only one, two or threestandard deviations from the mean K McMullen 2012
4. 4. Normal DistributionThe normal distribution always has the meandirectly in the middleThe standard deviations are evenly spaced fromthe mean99.97% of the data falls within 3 standarddeviations of the mean therefore, when drawingthe standard deviation, we tend to only go 3standard deviations below the mean and 3standard deviations above the mean K McMullen 2012
5. 5. Normal DistributionLooking within the standard deviationsThe 68-95-99.7% rule 68% of the values lie within 1 standard deviation of the mean 95% of the values lie within 2 standard deviations of the mean 99.7% of the values lie within 3 standard deviations of the mean K McMullen 2012
6. 6. Normal DistributionLooking above or below the standard deviations 16% is above 1 standard deviation from the mean 16% is below 1 standard deviation from the mean 2.5% is above 2 standard deviations from the mean 2.5% is below 2 standard deviations from the mean 0.15% is above 3 standard deviations from the mean 0.15% is below 3 standard deviations from the mean K McMullen 2012
7. 7. Normal DistributionStandard Scores (z-scores) The 68-95-99.97% rule makes the standard deviation a natural measuring stick for normally distributed data Standardising data allows us to see how a value relates to the mean The mean is 0, therefore: A positive z-score indicates the data value lies above the mean A zero z-score indicates the data value is equal to the mean A negative z-score indicates that the data value lies below the mean K McMullen 2012
8. 8. Normal DistributionCalculating a z-score: K McMullen 2012