Histogram and density plots in R Programming - Step-by-Step Execution

Concept Flow - Histogram and density plots

Start with data vector

↓

Choose plot type: Histogram or Density

↓

Histogram: Count data in bins

↓

Draw bars for each bin

↓

Density: Estimate smooth curve

↓

Draw smooth density line

↓

Display plot

Start with data, choose histogram or density plot, then either count data in bins for bars or estimate a smooth curve, and finally display the plot.

Execution Sample

R Programming

data <- c(2,3,3,5,7,8,8,9,10)
hist(data, breaks=5, col='skyblue')
density_data <- density(data)
plot(density_data, col='red')

This code creates a histogram with 5 bins and a blue color, then calculates and plots a red density curve of the same data.

Execution Table

Step	Action	Input/Condition	Result/Output
1	Create data vector	data = c(2,3,3,5,7,8,8,9,10)	Data vector ready with 9 values
2	Call hist()	breaks=5 bins	Data divided into 5 bins: [2-3.6), [3.6-5.2), [5.2-6.8), [6.8-8.4), [8.4-10]
3	Count values in bins	Bin 1: 2,3,3	Count = 3
4	Count values in bins	Bin 2: 5	Count = 1
5	Count values in bins	Bin 3: 7	Count = 1
6	Count values in bins	Bin 4: 8,8	Count = 2
7	Count values in bins	Bin 5: 9,10	Count = 2
8	Draw histogram bars	Counts per bin	Bars drawn with heights 3,1,1,2,2 in skyblue
9	Calculate density	density(data)	Density object with x and y values for smooth curve
10	Plot density	plot(density_data)	Smooth red density curve drawn over data range
11	End	All plots drawn	Histogram and density plot displayed

💡 All data processed and both plots rendered successfully

Variable Tracker

Variable	Start	After Step 2	After Step 9	Final
data	empty	c(2,3,3,5,7,8,8,9,10)	same	same
histogram_bins	none	[2-3.6), [3.6-5.2), [5.2-6.8), [6.8-8.4), [8.4-10]	same	same
bin_counts	none	[3,1,1,2,2]	same	same
density_data	none	none	density object with x,y	same

Key Moments - 3 Insights

Why does the histogram have 5 bars even though there are 9 data points?

Because the 'breaks=5' argument divides the data range into 5 bins, and the histogram counts how many data points fall into each bin, not one bar per data point. See execution_table rows 2-7.

What is the difference between histogram bars and the density curve?

Histogram bars show counts of data in fixed bins (rows 3-7), while the density curve is a smooth estimate of data distribution (rows 9-10). They represent data differently but both show data shape.

Why do we need to calculate 'density(data)' before plotting?

The density() function computes x and y values for the smooth curve. Without it, plot() cannot draw the density line. See execution_table row 9.

Visual Quiz - 3 Questions

Look at the execution table, how many data points fall into the first histogram bin?

A 2

B 3

C 1

D 5

💡 Hint

Check execution_table row 3 where bin 1 count is shown.

At which step is the smooth density curve calculated?

A Step 2

B Step 5

C Step 9

D Step 11

💡 Hint

Look at execution_table row 9 describing density calculation.

If we change breaks=5 to breaks=3 in hist(), what happens to the bin counts?

A Fewer bins with more counts each

B More bins with fewer counts each

C Same number of bins and counts

D Histogram will not draw

💡 Hint

Refer to variable_tracker 'histogram_bins' and how breaks control bin count.

Concept Snapshot

Histogram and density plots in R:
- Use hist(data, breaks=n) to create histogram with n bins.
- Histogram counts data points in bins and draws bars.
- Use density(data) to estimate smooth distribution curve.
- Plot density object with plot() to see smooth line.
- Both visualize data shape differently but complement each other.

Full Transcript

This visual execution trace shows how to create histogram and density plots in R. We start with a data vector of numbers. The hist() function divides data into bins (here 5 bins) and counts how many data points fall into each bin. These counts become the heights of bars drawn in the histogram. Then, the density() function calculates a smooth curve estimating the data distribution. Plotting this density object draws a smooth red line. The execution table steps through creating data, binning, counting, drawing bars, calculating density, and plotting the curve. Variable tracking shows how data and counts change. Key moments clarify common confusions about bins vs data points and histogram vs density. The quiz tests understanding of bin counts, density calculation step, and effect of changing bin numbers. The snapshot summarizes syntax and behavior for quick reference.

Practice

1. What is the main difference between a histogram and a density plot in R?

easy

A. Histogram shows exact values; density plot shows counts only.

B. Histogram uses bars; density plot uses a smooth curve.

C. Histogram is for categorical data; density plot is for numeric data.

D. Histogram requires ggplot2; density plot does not.

Solution

1. Step 1: Understand histogram representation

   A histogram displays data grouped into bins using bars to show frequency counts.

2. Step 2: Understand density plot representation

   A density plot shows a smooth curve estimating the data distribution, not bars.

3. Final Answer:

   Histogram uses bars; density plot uses a smooth curve. -> Option B

4. Quick Check:

   Histogram = bars, Density plot = smooth curve [OK]

Hint: Bars mean histogram; smooth curve means density plot [OK]

Common Mistakes:

• Thinking histogram shows exact values instead of grouped counts
• Confusing density plot with bar charts
• Assuming histograms only work with categorical data

2. Which of the following is the correct R code to create a histogram of the numeric vector data?

easy

A. hist(data)

B. plot.histogram(data)

C. histogram(data)

D. density(data)

Solution

1. Step 1: Recall the base R function for histograms

   The correct function to create a histogram in base R is hist().

2. Step 2: Check the options

   Only hist(data) is valid syntax; others are either incorrect function names or for density plots.

3. Final Answer:

   hist(data) -> Option A

4. Quick Check:

   hist() creates histograms in R [OK]

Hint: Use hist() for histograms in base R [OK]

Common Mistakes:

• Using non-existent function histogram()
• Confusing density() with hist()
• Trying plot.histogram() which is invalid

3. What will be the output of the following R code?

set.seed(1)
data <- rnorm(100)
hist(data, breaks=5, col='blue')

medium

A. An error because breaks cannot be numeric

B. A density plot with 5 blue lines

C. A histogram with 5 blue bars showing data distribution

D. A scatter plot of 100 points

Solution

1. Step 1: Understand hist() with breaks parameter

   The breaks=5 argument divides data into 5 bins for the histogram.

2. Step 2: Check color and plot type

   The col='blue' colors the bars blue; hist() creates a bar plot, not a density or scatter plot.

3. Final Answer:

   A histogram with 5 blue bars showing data distribution -> Option C

4. Quick Check:

   hist() + breaks=5 + col='blue' = blue bars histogram [OK]

Hint: breaks sets bar count; col sets bar color [OK]

Common Mistakes:

• Thinking breaks=5 creates density plot
• Assuming breaks cannot be numeric
• Confusing hist() with scatter plot

4. Identify the error in this R code for plotting a density plot:

data <- rnorm(50)
density(data, col='red')

medium

A. density() does not accept a col argument directly

B. rnorm() cannot generate 50 values

C. Missing parentheses after density

D. data must be a data frame, not a vector

Solution

1. Step 1: Check density() function usage

   The density() function returns density data but does not plot directly or accept col.

2. Step 2: Correct plotting method

   To plot with color, use plot(density(data), col='red') instead.

3. Final Answer:

   density() does not accept a col argument directly -> Option A

4. Quick Check:

   density() returns data; plot() colors it [OK]

Hint: Use plot(density()) to color density plots [OK]

Common Mistakes:

• Passing col directly to density()
• Thinking density() plots automatically
• Assuming rnorm() can't generate 50 values

5. You want to compare the distribution of two numeric vectors x and y in R using a single plot. Which code correctly overlays their density plots with different colors?

hard

A. plot(density(x, col='blue'), density(y, col='red'))

B. hist(x, col='blue'); hist(y, col='red')

C. density(x, col='blue'); density(y, col='red')

D. plot(density(x), col='blue'); lines(density(y), col='red')

Solution

1. Step 1: Plot first density with plot()

   Use plot(density(x), col='blue') to draw the first density curve in blue.

2. Step 2: Add second density with lines()

   Use lines(density(y), col='red') to overlay the second density curve in red.

3. Final Answer:

   plot(density(x), col='blue'); lines(density(y), col='red') -> Option D

4. Quick Check:

   plot() then lines() overlays densities with colors [OK]

Hint: plot() first density, lines() add second [OK]

Common Mistakes:

• Using hist() which creates separate plots
• Passing col to density() instead of plot() or lines()
• Trying to plot both densities in one plot() call