Descriptive statistics in R Programming - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the purpose of descriptive statistics?

Descriptive statistics summarize and describe the main features of a dataset using numbers and graphs, making data easier to understand.

beginner

Name three common measures of central tendency.

The three common measures are mean (average), median (middle value), and mode (most frequent value).

beginner

What does the standard deviation tell us about data?

Standard deviation shows how spread out the data is around the mean. A small value means data points are close to the mean; a large value means they are spread out.

beginner

In R, which function gives a quick summary of a dataset including min, max, median, and quartiles?

The function summary() provides a quick overview of these statistics for each column in a dataset.

intermediate

What is the difference between variance and standard deviation?

Variance measures the average squared distance from the mean, while standard deviation is the square root of variance, giving spread in the original units.

Which measure of central tendency is least affected by extreme values?

A Mean

B Range

C Mode

D Median

The median is the middle value and is not influenced by very high or low values, unlike the mean.

What does the function sd() in R calculate?

A Median

B Standard deviation

C Mean

D Variance

sd() calculates the standard deviation, which measures data spread around the mean.

Which of the following is NOT a measure of spread?

A Mean

B Variance

C Range

D Standard deviation

Mean is a measure of central tendency, not spread.

What does the summary() function in R return for numeric data?

A Only mean and median

B Only standard deviation

C Min, 1st quartile, median, mean, 3rd quartile, max

D Only mode

summary() returns a set of descriptive statistics including min, quartiles, median, mean, and max.

If data points are very close to the mean, what can we say about the standard deviation?

A It is small

B It is zero

C It is large

D It is negative

A small standard deviation means data points are close to the mean.

Explain the main types of descriptive statistics and their roles in understanding data.

Think about how we describe the center and spread of data.

Describe how you would use R functions to get a quick overview of a dataset's descriptive statistics.

Focus on common R functions for descriptive stats.

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