Descriptive statistics in R Programming

Introduction

Descriptive statistics help us understand data by summarizing it with simple numbers and tables.

To find the average score of students in a class.

To see how spread out daily temperatures are in a city.

To check the most common category in survey answers.

To quickly summarize sales numbers for a product.

To compare heights of people in two groups.

Syntax

R Programming

mean(x)
median(x)
var(x)
sd(x)
summary(x)
table(x)

x is your data vector or column.

summary() gives min, 1st quartile, median, mean, 3rd quartile, max.

Examples

Calculate the average of numbers in x.

R Programming

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

Find the middle value in x.

R Programming

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

Calculate variance and standard deviation to see data spread.

R Programming

x <- c(2, 4, 6, 8, 10)
var(x)
sd(x)

Count how many times each fruit appears.

R Programming

x <- c('apple', 'banana', 'apple', 'orange', 'banana')
table(x)

Sample Program

This program calculates basic descriptive statistics for a small set of numbers.

R Programming

data <- c(5, 7, 8, 9, 10, 10, 12, 15, 18, 20)

cat('Mean:', mean(data), '\n')
cat('Median:', median(data), '\n')
cat('Variance:', var(data), '\n')
cat('Standard Deviation:', sd(data), '\n')
cat('Summary:', '\n')
print(summary(data))

Important Notes

Missing values (NA) can cause errors; use na.rm=TRUE inside functions to ignore them.

Variance and standard deviation measure spread; variance is in squared units, standard deviation in original units.

Summary

Descriptive statistics summarize data with simple numbers.

Common measures include mean, median, variance, and standard deviation.

Use summary() for a quick overview of numeric data.

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