1.3 Density Curves and Normal Distributions. What is a density curve?. Idea of density. Density curve describes an overall pattern. Area under the curve should give a probability- hence, total area under a density curve is always 1. We would like to model real life data by a density curve.
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Density curve describes an overall pattern.
Area under the curve should give a probability- hence, total area under a density curve is always 1.
We would like to model real life data by a density curve.
Whenever we use a histogram to approximate a density curve, we must be careful to distinguish between the mean of the sample vs. the mean of the population. Likewise for standard deviation.
We use x for the mean of the sample and the Greek letter μ (mu) for the mean of the population. Note that while we may never know μ, it does exist. We use s for standard deviation of sample and σ (sigma) for the population standard deviation.
When a density distribution is symmetric, we say this is a normal distribution.
Normal distributions can have different shapes.
It turns out that a normal curve is completely determined by the mean and standard deviation.
Mean is at the maximum point.
1 Standard deviation is where the curve changes “concavity.”
How can we tell if data is approximately normal?
Use a normal quantile plot.
Idea: Plot each point against its normal score. The closer to a straight line, the more likely the data is normal.
Best done on a computer.