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).

Practice

1. Which of the following best describes the mean in descriptive statistics?

easy

A. The average value of a numeric dataset

B. The middle value when data is sorted

C. The most frequent value in the dataset

D. The difference between the largest and smallest values

Solution

1. Step 1: Understand the definition of mean

   The mean is calculated by adding all numbers and dividing by the count.

2. Step 2: Compare with other options

   Median is the middle value, mode is most frequent, range is difference between max and min.

3. Final Answer:

   The average value of a numeric dataset -> Option A

4. Quick Check:

   Mean = Average [OK]

Hint: Mean is sum divided by count, simple average [OK]

Common Mistakes:

• Confusing mean with median
• Thinking mean is the most frequent value
• Mixing mean with range

2. Which R function gives a quick summary including min, 1st Qu., median, mean, 3rd Qu., and max for numeric data?

easy

A. mean()

B. var()

C. sd()

D. summary()

Solution

1. Step 1: Recall function purposes

   mean() calculates average, var() variance, sd() standard deviation.

2. Step 2: Identify summary function

   summary() provides min, quartiles, median, mean, and max in one output.

3. Final Answer:

   summary() -> Option D

4. Quick Check:

   summary() = quick overview [OK]

Hint: summary() shows min, quartiles, median, mean, max [OK]

Common Mistakes:

• Using mean() expecting full summary
• Confusing sd() with summary()
• Trying var() for descriptive summary

3. What is the output of this R code?

data <- c(4, 8, 6, 5, 3, 7)
mean(data)

medium

A. 5.5

B. 6

C. 4.5

D. 5

Solution

1. Step 1: Sum the data values

   4 + 8 + 6 + 5 + 3 + 7 = 33

2. Step 2: Divide sum by number of values

   There are 6 values, so 33 / 6 = 5.5

3. Final Answer:

   5.5 -> Option A

4. Quick Check:

   Mean = 33/6 = 5.5 [OK]

Hint: Add all numbers, divide by count [OK]

Common Mistakes:

• Adding incorrectly
• Dividing by wrong count
• Confusing mean with median

4. Identify the error in this R code for calculating variance:

data <- c(2, 4, 6, 8)
var_data <- var(data, na.rm=TRUE)
print(var_data)

medium

A. Missing parentheses in var() function

B. No error, code runs correctly

C. na.rm argument is invalid for var()

D. Variable data is not defined

Solution

1. Step 1: Check variable definition

   data is defined as a numeric vector correctly.

2. Step 2: Verify var() usage

   var() accepts na.rm=TRUE to remove missing values; syntax is correct.

3. Final Answer:

   No error, code runs correctly -> Option B

4. Quick Check:

   var() with na.rm=TRUE is valid [OK]

Hint: var() accepts na.rm=TRUE to ignore NAs [OK]

Common Mistakes:

• Thinking na.rm is invalid for var()
• Assuming missing parentheses error
• Not defining data before use

5. You have a numeric vector v <- c(10, 20, 30, NA, 40, 50). Which R code correctly calculates the mean ignoring the missing value?

hard

A. mean(na.exclude(v))

B. mean(v, na.rm=TRUE)

C. Both B and C

D. mean(v)

Solution

1. Step 1: Understand missing value handling

   By default, mean() returns NA if vector has NA values.

2. Step 2: Check options to ignore NA

   mean(v, na.rm=TRUE) removes NA before calculation. mean(na.exclude(v)) also removes NA values before calculation, so it returns the mean ignoring NA as well. mean(v) returns NA.

3. Final Answer:

   Both mean(v, na.rm=TRUE) and mean(na.exclude(v)) -> Option C

4. Quick Check:

   na.rm=TRUE and na.exclude() both remove NA for mean calculation [OK]

Hint: Use na.rm=TRUE or na.exclude() to ignore NA [OK]

Common Mistakes:

• Using mean() without na.rm=TRUE returns NA
• Not removing NA before mean calculation
• Confusing na.rm with na.exclude