Summarizing data: Mean, standard deviation etc.
For continuous variables, we can look at the mean and standard deviation.
Picking on the displacement column from the MPG dataset, take a wild guess at how you would calculate the mean and standard deviation.
You use the mean command to compute the mean and SD for the standard deviation.
Picking on the displacement column from the MPG dataset, take a wild guess at how you would calculate the mean and standard deviation.
You use the mean command to compute the mean and SD for the standard deviation.
Here are the results
mean(mpg$displ) [1] 3.471795
sd(mpg$displ) [1] 1.291959
Statisticians often talk about the five number summary, which describes a distribution of data in just five numbers. These are the sample minimum, or the smallest value, the first, or lower, quartile, the median, or middle, value, the third, or upper quartile, and the sample maximum, or the largest value.
R makes the five number summary incredibly simple.
You type 'summary', like this
summary((mpg$displ))
Min. 1st Qu. Median Mean 3rd Qu. Max.
1.600 2.400 3.300 3.472 4.600 7.000
Notice that summary is so good that you get a sixth number, the mean, for free.
If you really want just the five numbers, use the fivenum command
If you really want just the five numbers, use the fivenum command
fivenum(mpg$displ)
[1] 1.6 2.4 3.3 4.6 7.0
This gives us a fairly good idea of what this data set looks like, but a picture tells a thousand words
and we can visualize the entire distribution by creating a histogram using ggplot.
and we can visualize the entire distribution by creating a histogram using ggplot.
If you type these commands, you'll get this picture
ggplot(mpg,aes(displ))+
geom_histogram(col="black")+
theme(text=element_text(size=30))
![](data:image/png;base64,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)
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