Day5–Histograms, Scatter Plots, Outliers

Today’s Agenda

• Finish Box Plots
• Histograms
• Scatter Plots
• Standard deviation

Outlier in Chinstrap data

To begin with, filter out a data frame that only has the Chinstrap penguins in it:

# look at the data
penguins_data <- penguins

# Filter Chinstrap
chinstrap <- filter(penguins, species == "Chinstrap")

Now plot a box plot for the body mass of Chinstrap penguins:

# Body mass boxplot for Chinstrap penguins
ggplot(chinstrap, aes(y = body_mass_g)) + geom_boxplot()

Now compute the quantiles for the body mass of Chinstrap penguins

# quantiles for body mass of Chinstrap penguins
quantile(chinstrap$body_mass_g)

##     0%    25%    50%    75%   100% 
## 2700.0 3487.5 3700.0 3950.0 4800.0

Finally, compute the size of the whiskers by doing $Q_3 + 1.5 \times IQR$ and $Q_1 - 1.5 \times IQR$

# compute the size of the whiskers
IQR <- 3950 - 3487.5
IQR(chinstrap$body_mass_g)

## [1] 462.5

3950 + 1.5*IQR

## [1] 4643.75

3487.5 - 1.5*IQR

## [1] 2793.75

ggplot(penguins, aes(y=body_mass_g)) +
  geom_boxplot() + 
  facet_wrap(~species)

## Warning: Removed 2 rows containing non-finite values (stat_boxplot).

ggplot(penguins, aes(y=body_mass_g, color=species)) +
  geom_boxplot() 

## Warning: Removed 2 rows containing non-finite values (stat_boxplot).

Histograms

ggplot(penguins, aes(x = body_mass_g)) + geom_histogram(binwidth = 50)

## Warning: Removed 2 rows containing non-finite values (stat_bin).

Scatterplots

Standard Deviation

$$\text{standard deviation} = \sqrt{\text{variance}} = \sqrt{\sigma^2} = \sigma = \sqrt{\displaystyle \frac{\sum_{i=1}^n (\mu-x_i)^2}{N}}$$

Standard deviation in a Sample

$$\text{standard deviation} = \sqrt{\text{variance}} = \sqrt{s^2} = s = \sqrt{\displaystyle \frac{\sum_{i=1}^n (\bar{x}-x_i)^2}{n-1}}$$