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Basic Statistics

R lab - Exploring data

Checking the dimensions of your data

Q1. #Use the dim() function on mtcars

Answer:- dim(mtcars) 

Data Structure

Q.2 According to R, what type of variable is am?

Answer factor

 

Levels

Q.3 # Look at the levels of the variable am

Answer  levels(mtcars$am)

 

Recoding Variables

Q #Assign the value of mtcars to the new variable mtcars2

mtcars2 <- mtcars

Q #Assign the label "high" to mpgcategory where mpg is greater than or equal to 20

mtcars2$mpgcategory[mtcars2$mpg >= 20] <- "high"

Q #Assign the label "low" to mpgcategory where mpg is less than 20

mtcars2$mpgcategory[mtcars2$mpg < 20] <- "low"

Q #Assign mpgcategory as factor to mpgfactor

mtcars2$mpgfactor <- as.factor(mtcars2$mpgcategory)

Examining Frequencies

Q #How many of the cars have a manual transmission?

13

Cumulative Frequency

Q # What percentage of cars have 3 or 5 gears?

62.5

Making a Bar Graph

Q #Assign the frequency of the mtcars variable "am" to a variable called "height"

height <- table(mtcars$am)

Q #Create a barplot of "height"

barplot(height)

Labelling A Bar Graph

Q # vector of bar heights

height <- table(mtcars$am)

Q # Make a vector of the names of the bars called "barnames"

barnames <- c("automatic", "manual")

Q # Label the y axis "number of cars" and label the bars using barnames

barplot(height, ylab = "number of cars", names.arg = barnames)

Interpreting A Bar Graph

Q Based on the bar chart of transmission type that you made in the previous exercise, which type of transmission is most common? (remember, 0 = automatic, 1 = manual)

automatic

Histograms

Q # Make a histogram of the carb variable from the mtcars data set. Set the title to "Carburetors"

hist(mtcars$carb, main = "Carburetors")

Formatting Your Histogram

Q # arguments to change the y-axis scale to 0 - 20, label the x-axis and colour the bars red

hist(mtcars$carb, main = "Carburetors", ylim = c(0,20), xlab = "Number of Carburetors", col = "red")

Bar Graph vs. Histogram

Bar Graph vs. Histogram

50xp

Why did we make a bar graph of transmission (mtcars$am), but a histogram of carburetors (mtcars$carb)

Possible Answers

Because transmission is categorical, and carb is continuous

Distributions

50xp

Take a look at the distributions in these histograms. Which of the following is correct?

Possible Answers

Graph 1 is left skewed, graph 2 is normally distributed, graph 3 is right skewed.

Mean and Median

Q # Calculate the mean miles per gallon

mean(mtcars$mpg)

Q # Calculate the median miles per gallon

median(mtcars$mpg)

Mode

# Produce a sorted frequency table of `carb` from `mtcars`

sort(table(mtcars$carb), decreasing = TRUE)

Range

# Minimum value

x <- min(mtcars$mpg)

# Maximum value

y <- max(mtcars$mpg)

# Calculate the range of mpg using x and y

y – x

Quartiles

Q # What is the value of the second quartile?

17.7100

Q # What is the value of the first quartile?

16.8925

IQR and boxplot

Q # Make a boxplot of qsec

boxplot(mtcars$qsec)

Q # Calculate the interquartile range of qsec

IQR(mtcars$qsec)

IQR outliers

Q # What is the threshold value for an outlier below the first quartile?

13.88125

Q # What is the threshold value for an outlier above the third quartile?

21.91125

Standard Deviation

Q # Find the IQR of horsepower

IQR(mtcars$hp)

Q # Find the standard deviation of horsepower

sd(mtcars$hp)

Q # Find the IQR of miles per gallon

IQR(mtcars$mpg)

Q # Find the standard deviation of miles per gallon

sd(mtcars$mpg)

Mean, median and mode.

50xp

Mean, median and mode are all measures of the average. In a perfect normal distribution the mean, median and mode values are identical, but when the data is skewed this changes. In the the graph on the right which of the following statements are most accurate?

The mode is higher than the mean. It makes most sense to use the median to measure central tendency.

Calculating Z-scores

# Calculate the z-scores of mpg

(mtcars$mpg - mean(mtcars$mpg)) / sd(mtcars$mpg)

Distributions And Z-scores

50xp

In the distribution shown on the right, what percentage of data will fall between the z-scores of -2 and 2?

95 %

Z-score Outliers

50xp

Outside of which boundaries might an observation be considered an outlier?

-3 and 3