MATH 315 Homework 04

Due 2025-09-26 by 11:59pm

  1. Read in the dataset found at the following URL:

https://raw.githubusercontent.com/roualdes/data/refs/heads/master/finches.csv

The dataset is about finches (so I'm told, finches Darwin studied) and has a help file.

  1. Pick a numeric variable and print the first 7 observations using the R function head. Then print the last 10 observations using the function tail.

  2. Pick a numeric variable and calculate the mean and the median, using the functions mean and median. If one is bigger than the other, explain why that is probably the case.

  3. Justify your answer above with an appropriate histogram.

  4. Pick a numeric variable and calculate the standard deviation and the interquartile range, using the functions sd and IQR.

  5. Pick a numeric variable and calculate a quantile of your choice. Interpret this statistic in the context of the data.

  6. Use the dplyr functions summarise and group_by to calculate the following summary statistics on a numeric variable of your choice grouped by the variable island: mean, standard deviation, median, first quartile, third quartile, minimum, and maximum (use the functions min and max, respectively).

  7. Using your calculations in 6., what type of skew, if any, does your numeric variable have for each level of island? Why?

  8. Explain, in the context of these data, two of your summary statistics.

  9. Make box plots of your numeric variable split by the variable island.

  10. Use the dplyr function mutate to create a new ratio variable using any two numeric variables of your choice.

  11. Make box plots or histograms, whichever you prefer, split by the variable island of your new ratio variable. Explain one interesting aspect of this new numeric variable in context of the data.

  12. Give a real-world example of a Bernoulli distribution where . What might the probability for your example be?

  13. Give a real-world example of a Binomial distribution. What sort of probability questions might you ask of this Binomial distribution. Provide two such questions.

  14. Give a real-ish-world example of a Normal distirbution. What might the parameters be?