Histogram and density plots in R Programming - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Histogram bin count effect

What is the effect on the histogram when changing the number of bins in this R code?

R Programming

data <- c(1,2,2,3,3,3,4,4,4,4)
hist(data, breaks=2, plot=FALSE)$counts
hist(data, breaks=5, plot=FALSE)$counts

A [5, 5] and [0, 2, 3, 3, 2]

B [5, 5] and [2, 2, 2, 2, 2]

C [5, 5] and [1, 2, 2, 2, 3]

D [5, 5] and [1, 1, 2, 3, 3]

💡 Hint

Try running hist() with different breaks values and check the counts component.

With breaks=2, the data is split into two bins each containing 5 values. With breaks=5, the data is split into 5 bins with counts 0,2,3,3,2 respectively.

🧠 Conceptual

intermediate

Difference between histogram and density plot

Which statement correctly describes the difference between a histogram and a density plot in R?

A Histogram shows cumulative counts; density plot shows raw data points.

B Histogram shows a smoothed curve; density plot shows counts per bin.

C Histogram and density plot are identical visualizations with different names.

D Histogram shows counts per bin; density plot shows a smoothed estimate of the distribution.

💡 Hint

Think about what each plot type represents visually.

Histograms display counts or frequencies in bins, while density plots show a smooth curve estimating the probability density function.

🔧 Debug

advanced

Fix the error in density plot code

What error does this R code produce and why? density(data, bw="wrong") Assume data is a numeric vector.

A Error: 'bw' must be numeric or a function, not a character string.

B Error: object 'data' not found.

C Error: density() requires a data frame, not a vector.

D No error; code runs and plots density.

💡 Hint

Check the expected type for the 'bw' parameter in density().

The 'bw' parameter expects a numeric value or a function, not a character string. Passing "wrong" causes a type error.

❓ Predict Output

advanced

Overlay histogram and density plot

What will be the output of this R code snippet?

R Programming

set.seed(1)
data <- rnorm(100)
hist(data, freq=FALSE, col='lightblue')
density_data <- density(data)
lines(density_data, col='red')
length(density_data$x)

A 50

B 100

C 512

D 101

💡 Hint

Check the default length of the density() output vector in R.

The density() function by default returns 512 points for the x and y vectors representing the density curve.

🚀 Application

expert

Calculate area under density curve

Given a density object in R, which code correctly calculates the approximate area under the density curve?

A sum(density_data$x) * diff(density_data$y)[1]

B sum(density_data$y) * diff(density_data$x)[1]

C mean(density_data$y) * length(density_data$x)

D sum(density_data$y)

💡 Hint

Think about numerical integration using the trapezoidal rule approximation.

The area under the curve is approximated by summing the heights (y) times the width between x points. diff(density_data$x)[1] gives the uniform spacing.

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