Extra: CA1

Overview

Coverage: L01-L09, P1-P3

This is a document to give you additional practice working in R. It will include working with data (manipulating, summarising, plotting) and analyzing the distributions we’ve covered.

Please do not treat this as a comprehensive study guide for CA1!

Note that there are often many possible paths to the correct solution.

library(tidyverse); theme_set(theme_classic())
library(readxl)
set.seed(2026)

Iris

The iris dataset is available in R upon start-up.

What are the dimensions of the object (rows, columns) and what data type is it?

Create a scatter plot of sepal area on the x-axis and petal area on the y-axis.

For each species, what is the mean and standard deviation of sepal area?

Create a plot with two panels, each with a boxplot with species on the x-axis. In the first panel, plot sepal area on the y-axis. In the second panel, plot petal area on the y-axis.

Extract the even numbered rows from iris, and the columns Species, Sepal.Area, and Petal.Area in that order.

Air quality

The airquality dataset is available in R upon start-up, and gives daily values of mean ozone, solar radiation, mean wind speed, and max temperature at LaGuardia Airport in New York City (?airquality).

Make a histogram of wind speed.

Assume wind speed is normally distributed in this dataset with \(\mu=9.99 mph\) and \(\sigma = 3.51 mph\).

What proportion of days would you expect to have a wind speed less than 5 mph?

You have a kite that can only be flown safely in winds between 14 mph and 20 mph. What proportion of days would be suitable?

How many days would be suitable in a 31-day month?

What proportion of days in the dataset were actually suitable?

What are the z-scores for 14 and 20 mph?

What are the quantiles for the middle 95%?

What is the quantile for the largest 5%?

Given the population parameters above, what is the z score of the sample mean in the dataset?

Given the population parameters above, what is the probability of observing a sample mean smaller than the one in this dataset?

Create a scatter plot with temperature on the x-axis and log-transformed ozone on the y-axis.

Create a boxplot with the solar radiation on the y-axis and the month on the x-axis.

Coral predation

You are studying predation of the Flamingo Tongue Snail on soft corals on South Water Caye in Belize. In a distinct patch of reef, you randomly select a sample of 14 corals and identify that 9 of these have feeding scars.

What distribution would you expect this variable (i.e., the number of corals with feeding scars of those sampled) to follow?

What is your sample proportion and its standard error?

Create a bar graph of the binomial distribution corresponding to these parameters, with the x-axis spanning the full range of possible outcomes.

Based on this distribution, if you were to collect another random sample of the same size, what is the probability that all 14 would have feeding scars?

What is the probability you would find fewer with feeding scars than in the first sample?

What is the probability of finding more with feeding scars than in the first sample?

What is the probability of a sample with 4, 5, or 6 corals with feeding scars?

Earthquakes

The dataset quakes is available in R upon start-up, and gives magnitudes and locations for 1000 seismic events near Fiji since 1964.

Plot the locations of the earthquakes (x-axis: longitude, y-axis: latitude).

Create a column called mag_cat with the magnitude truncated to integer (i.e., 4.0-4.99 become 4). Hint: ?trunc

For each magnitude category (mag_cat), count the number of occurrences in the dataset.

Let’s assume the dataset spans 60 years (1964-2023). What is the mean number of magnitude category 5 earthquakes per year?

What distribution is most suitable for the number of category 5 earthquakes per year?

Using the above value as \(\lambda\), create a bar plot of the probability distribution of the number of category 5 earthquakes per year, ranging from 0 to 10 earthquakes.

What is the probability that next year has no category 5 earthquakes?

Of the next 10 years, how many would you expect to have:

No category 5 earthquakes?

Fewer than 2 earthquakes?

At least 5?