---
title: "Lab 6: Graphics"
author: 'Group Member Names - here'
date: "February 20, 2018"
output: html_document
---
Turn in one copy for each group. If group members are not present in class they will be required to complete their own lab to receive credit. Please turn in **both a DOC or PDF file and your R Markdown script**.  This is due on Sunday, February 25.

## Lab Overview



## Questions
Answer the following questions in this R Markdown document. Please include code where necessary.

### 1. Central Limit Theorem Example (50 points)

The central limit theorem is a foundational idea in statistical inference. Typically, it is assumed that the mean of a sample converges to a normal distribution when the sample size is greater than (20 or 30?). So where do these numbers come from? 

To look at this question, modify the function to also print a histrogram. For full credit your function should have appropriate titles, labels, and be aesthetically pleasing.

```{r}
CLT <- function(num.sims){
  # function that simulates uniform random numbers to illustrate the central limit theorem
  # ARGS: num.sims - the number of samples to average in central limit theorem
  # RETURNS: list containing the mean and standard deviation of the average of the samples
  #          SHOULD ALSO CREATE A HISTOGRAM, WITH APPROPRIATE TITLES
  num.replicates <- 10000 # how many times to repeat this process
  samples <- rep(0, num.replicates)
  for (i in 1:num.replicates){
    samples[i] <- mean(runif(num.sims, min = 0, max = 100))
  }
  # CREATE HISTOGRAM HERE
  return(list(mean(samples), sd(samples)))
}
```


Demonstrate the function works by calling the function with 10, 30, 100, and 1000 samples. Briefly discuss the differences in these figures/results.

### 2. (50 points)

Download the data set on earthquakes, provided by the USGS, available at [http://www.math.montana.edu/ahoegh/teaching/stat408/datasets/EarthquakesAll.csv](http://www.math.montana.edu/ahoegh/teaching/stat408/datasets/EarthquakesAll.csv). The data set contains earthquakes from 1965 to 2016.

Create a compelling graphic from this data set. The choice of what and how is completely up to you. Then provide a short summary of the story your graphic depicts.