Math1005

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Week 4 Notes

The normal curve

It approximates many natural phenomenon

Does this by combining a large number of independent variables

Bellshaped curve

It represents a normal distribution

Standard Normal Curve

Has mean 0 and SD 1

Finding the area under a Standard Normal Curve

Integration of the formula

RStudio: pnorm function

pnorm (0.8) gets the red area

pnorm(0.8, lower.tail = F) gets the other side

pnorm(0.8) – pnorm(0.3) gets the area interval between 0.8 and 0.3

RStudio: different application of pnorm function (for nonstandard curves)

pnorm(x, mean, sd) where x is the point u want to get the area from

Interesting Properties of the Normal Curve

68% of the curve is within 1 sd from the middle

95% of the curve is within 2 sds from the middle

99.7% of the curve is within 3 sds from the middle

Measurement Error

Every measurement that is made could have turned out differently, this is due to chance error

Individual measurement = exact value + chance error

Estimating Chance Error

Replicating the measurement under the same conditions and calculating the standard deviation

Outliers

Small percentage of extreme measurements are known as outliers

They are conventionally defined by being more than 3 sds away from the mean

Bias

Constant amount added to or subtracted from each measurement

It can be deliberate or accidental

Individual measurement = exact value + chance error + bias

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Week 5 Notes