Descriptive statistics in R Programming - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Calculate the mean and median of a numeric vector

What is the output of this R code that calculates the mean and median of the vector c(2, 4, 6, 8, 10)?

R Programming

x <- c(2, 4, 6, 8, 10)
mean_x <- mean(x)
median_x <- median(x)
c(mean_x, median_x)

A [1] 5 5

B [1] 6 5

C [1] 5 6

D [1] 6 6

💡 Hint

Recall that mean is the average and median is the middle value when sorted.

The mean of the vector (2+4+6+8+10)/5 is 6. The median is the middle value in the sorted vector, which is also 6.

❓ data_output

intermediate

Count the number of unique values in a factor

Given the factor f <- factor(c('apple', 'banana', 'apple', 'orange', 'banana', 'banana')), what is the output of length(levels(f))?

R Programming

f <- factor(c('apple', 'banana', 'apple', 'orange', 'banana', 'banana'))
length(levels(f))

A 1

B 2

C 3

D 6

💡 Hint

Levels represent unique categories in a factor.

The factor has three unique categories: 'apple', 'banana', and 'orange'. So, length(levels(f)) returns 3.

❓ visualization

advanced

Interpret a boxplot of numeric data

What does the boxplot of the numeric vector c(1, 2, 2, 3, 4, 5, 6, 7, 8, 20) show about the data distribution?

R Programming

x <- c(1, 2, 2, 3, 4, 5, 6, 7, 8, 20)
boxplot(x, main = 'Boxplot of x')

A The boxplot shows a left-skewed distribution with an outlier at 1.

B The boxplot shows a right-skewed distribution with an outlier at 20.

C The boxplot shows a symmetric distribution with no outliers.

D The boxplot shows uniform distribution with no outliers.

💡 Hint

Look for the position of the median and any points outside whiskers.

The value 20 is much larger than the rest, so it appears as an outlier on the right side, indicating right skewness.

🧠 Conceptual

advanced

Understanding variance and standard deviation

Which statement correctly describes the relationship between variance and standard deviation?

A Standard deviation is the square root of variance, both measure data spread.

B Variance is the square root of standard deviation, both measure central tendency.

C Variance and standard deviation are unrelated statistics.

D Standard deviation is always larger than variance.

💡 Hint

Think about how variance and standard deviation relate mathematically.

Variance measures spread as average squared deviation; standard deviation is its square root, giving spread in original units.

🔧 Debug

expert

Identify the error in calculating the mode

What error does this R code produce when trying to calculate the mode of vector v <- c(1, 2, 2, 3, 4) using mode_v <- mode(v)?

R Programming

v <- c(1, 2, 2, 3, 4)
mode_v <- mode(v)
mode_v

A It returns the storage mode of the vector, not the statistical mode.

B It raises a syntax error because mode() is not a valid function.

C It returns the most frequent value correctly.

D It returns NULL because the vector is numeric.

💡 Hint

Check what the mode() function returns in R base.

In R, mode() returns the type of storage (like 'numeric'), not the statistical mode (most frequent value).