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.