1. Evaluate whether rounded measurements are odd numbers or even number each.
2. Count the N of even number using the results above.
3. sumbit the number to the following.

iris.tidy %>% 
  mutate(round.measurement = 
           round(measurement, digits = 0)%%2) %>% 
  dplyr::filter(round.measurement == 1) %>% 
  nrow()

## [1] 280

• A figure (graph) showing shape of density
• Difference from histogram
  • histogram: both continuous and discrete numbers
  • density plot: merely for continuous numbers

• A comprehensive package to draw figures such as graph and maps
• Much more flexible and friendly with academic publication in comparison with base::plot() function

1. Make plot area and fix type of graph
2. Arrange attributes, theme, and others
3. Assign the figure into a value
4. Save the figure

• A world-famous data set
  • The data set includes 5 attributes; Sepal.Length, Sepal.Width, Petal.Length, Petal.Width, and Species.
  • We use the data set frequently for practices such as drawing figures, clustering, ANOVA, and others.

  iris.tidy %>% 
  ggplot2::ggplot(aes(x = measurement,
                      y = ..density..,
                      fill = Species)
  ) +
  geom_density(alpha = 0.5, 
               colour = "black", 
               position = "identity"
  )

• The figure should be plotted by both attribute and species
• Labels of axes should be corrected.
• The legend should be replaced insude of plot area.
• Background color and grid are not necessary.

iris.tidy.density <- 
  iris.tidy %>% ggplot2::ggplot(aes(x = measurement,
                                    y = ..density..,
                                    fill = Species
                                    )
                                ) +
  geom_density(alpha = 0.5, colour = "black", position = "identity"
  ) +
  facet_wrap( ~ attribute, scale = "free_y") +
  labs(x = "Length", y = "Density")

iris.tidy.density <-   
iris.tidy.density +
  scale_fill_hue(name = "Species", 
                 labels = c("setosa" = "St.", 
                            "versicolor" = "Vc.",
                            "virginica" = "Ve."
                            )
  ) +
  theme_classic()

• Assign the figure into a value
• Using ggplot2::ggsave() function, save it.
  • In detail of the function, Check and refer to help message.
  • ?ggplot::ggsave

• Open your project folder and find the saved file.
• Adjust arguments as you like and compare with.

ggplot2::ggsave(filename =  "iris.density.pdf", 
                plot = iris.tidy.density,
                units = "mm", 
                dpi = 300
                )

• Using wine data set, make a density plot following constraints below.
  1. Transform the data set into tidy.
  2. Change filling color by Type.
  3. Save it with .pdf format and submit.
• To use the data set, install rattle.data package.

1. A discipline / subject　統計学
2. A indicator expressing characteristics of distribution　統計量

• To estimate a population’s distribution from sample distribution
• Statistics: parameters demonstrating characteristics of distribution
  • central tendency
  • variance
  • others

• Most frequently-used statistics indicating central tendency
  • \(\mu\): population mean
• Equivalent to centroid in Physics

\[ \bar{x} = \frac{1}{n}\sum_{i=1}^{n}x_{i} \] Where

n: sample size (N. of observation); i: index; \(x\): sample (observation / data)

• sample mean \(\bar{x}\) is not always the same as population mean \(\mu\).
• As the \(n\) become larger, the \(\bar{x}\) drifts.
• We need to consider the following conditions.
  • Variance of data
  • \(n\)

• A statistics indicating variance of observations / data.
  • Square root of variance \(\sigma^{2}\) \[ \sigma = \frac{1}{n}\sum_{i=1}^{n}(x_{i}-\bar{x}) \]
  • Mean is a point minimizing the deviation. ## Standard error (SE)
• Depending on sample size (N), the sample mean (\(\bar{x}\)) drifts.

• Blue: 100 observations from \(N(0, 1^{2})\)
• Grey: 10,000 observations from \(N(0, 1^{2})\)

• To adjust the influence of \(N\) toward mean, we need to consider \(SE\)
• The statistics suggests: the mean become more precise as the \(n\) increases.

\[ SE = \frac{sd}{\sqrt{n}} \]

• Mean: mean()
• SD: sd()
• Example: Compute the mean and SD of Sepal.Length of iris data

• Other statistics should be considered.
  • min()
  • max()
  • median():robust against outliers
• Stratification
• Making a summary table is essential.

iris.tidy %>% 
  dplyr::group_by(Species, attribute) %>%
  dplyr::summarise(n = n(),
                   Min. = min(measurement),
                   Max. = max(measurement),
                   Mean = mean(measurement),
                   Median = median(measurement),
                   SD = sd(measurement),
                   SE = sd(measurement) / sqrt(n())
  )

• Using the wine data set, make a summary table by type and attribute.