Combining Histogram and Density Plot

Fahim | 2023-11-01

Visualization is fundamental in gaining insights and understanding the data, yet selecting an appropriate visualization method can often pose a challenge.

Today I explore combining a histogram (showing the frequency of values of the continuous data within specific intervals) and a density plot (illustrating probability distribution).

Required Packages and Sample Data

if(!require(dplyr)){install.packages("dplyr")}
if(!require(ggplot2)){install.packages("ggplot2")}

theme_set(theme_bw())
set.seed(42)
df <- data.frame(
  continuous_var = rnorm(500, mean = 30, sd = 20)
)

Creating a Histogram

Let’s start by visualizing the distribution of data using a histogram.

n_bin = 20
df %>% 
  ggplot(aes(x = continuous_var, y = after_stat(count))) +
  geom_histogram(binwidth = n_bin, fill = "skyblue", color = "black") +
  labs(x = NULL, title = "Histogram")

Creating a Density Plot

Next, generate a density plot to illustrate the probability distribution of the data.

df %>% 
  ggplot(aes(x = continuous_var)) +
  geom_density(color = "red", linewidth = 1) +
  labs(x = NULL, title = "Density")

Combining Histogram and Density Plot

Now, let’s combine both graphs. Initially, there’s an issue as the histogram uses ‘count’ on the y-axis, while the density plot employs density distribution on the y-axis. Thus, resulting to below graph.

n_bin = 20

df %>% 
  ggplot(aes(x = continuous_var, y = after_stat(count))) +
  geom_histogram(binwidth = n_bin, fill = "skyblue", color = "black") +
  geom_density(color = "red", linewidth = 1) +
  labs(x = NULL, title = "Histogram & Density - 1")

To address this, I’ll rescale the density values so that the curve matches the y-axis scale of the histogram.

n_bin = 20
max_hist_bin <- max(table(cut(df$continuous_var, breaks = seq(min(df$continuous_var), max(df$continuous_var), by = n_bin))))
max_density_y <- max(density(df$continuous_var)$y)

df %>% 
  ggplot(aes(x = continuous_var, y = after_stat(count))) +
  geom_histogram(binwidth = n_bin, fill = "skyblue", color = "black") +
  geom_density(aes(y = after_stat(density) * max_hist_bin / max_density_y), color = "red", linewidth = 1) +
  labs(x = NULL, title = "Histogram & Density - 2")

Lastly I want to incorporate both count and density values. Thus, I add a secondary y-axis with the actual density values rather than the scaled values.

n_bin = 20
max_hist_bin <- max(table(cut(df$continuous_var, breaks = seq(min(df$continuous_var), max(df$continuous_var), by = n_bin))))
max_density_y <- max(density(df$continuous_var)$y)

df %>% 
  ggplot(aes(x = continuous_var, y = after_stat(count))) +
  geom_histogram(binwidth = n_bin, fill = "skyblue", color = "black") +
  geom_density(aes(y = after_stat(density) * max_hist_bin / max_density_y), color = "red", linewidth = 1) +
  scale_y_continuous(sec.axis = sec_axis(~ . * max_density_y / max_hist_bin, name = "density")) +
  labs(x = NULL, title = "Histogram & Density - 3")

This combination helps us to understand the frequency of values within specific intervals and to have a fuller picture of how the data is distributed, making analysis more insightful.