What’s normal?

The normal distribution is a curve we often see in real data.
- We see it in people’s blood pressures and in measurement errors.
When data appears to be normally distributed, we can use the normal model to:
- Simulate normally distributed data.
- Easily compute probabilities.
In this lab, we’ll look at some previous data sets to see if we can find data that are roughly normally distributed.

The normal distribution

The normal distribution is symmetric about the mean:
- The mean is found in the very center of the distribution.
- And the curve looks the same to the left of the mean as it does on the right.
Use the following to draw a normal distribution:

plotDist('norm', mean = 0, sd = 1)

To draw a normal curve, we need to know exactly 2 things:
- The mean and sd.
The sd, or standard deviation, is a measure of spread that’s similar to the MAD.
Which part of the normal curve changes when the value of the mean changes?
Which part of the normal curve changes when the value of the sd changes?
Hint: Try changing the mean and sd values in the plotDist function.

Load the cdc data and use the histogram function to answer the following:
Based on what you know about these variables, which of the variables do you think have distributions that will look like the normal distribution?
- Make histograms of these variables. Which ones look like the normal distribution?
- Hint: To help answer this question, try including the option fit = "normal" in the histogram function. You might also try faceting by gender.

Data scientists like using normal models because it often resembles real data.
- But not EVERYTHING is normally distributed.
As a data scientist in training, you must decide when a normal model seems appropriate.
- No model is ever perfect 100% of the time.
- If you choose a model, you should be able to justify why you chose it.

For each of the following, determine which, if any, appear to be normally distributed. Explain your reasoning:
- The weight of people in our cdc data, faceted by gender.
- The difference in mean weights between Males and Females for 500 random shuffles.
- The difference in median weights between Males and Females for 500 random shuffles.