In this lab you will use specific functions to determine the quartiles of a set of data. Quartiles of a set is defined as the 25%, 50% and 75% values of the dataset.

We can intepret this to mean the following:

In a sorted data set, the 25% value separates the lowest 25% of the set from the upper 75% of the set. The 50% value separates the lowest 50% of the set from the upper 50% of the set (often called the median). The 75% value separates the lower 75% from the upper 25% of the set.

If we think about how to calculate quartiles we could:

Find the median of the set

Separate out the set into two smaller sets

Find the medians of the smaller two sets

Load the Data

Your first task is to load a dataset from the file "mayoralpayroll.mat". Inside this file is a 177x5 array named payInfo containing salaries (among other things) of all the people working in the Mayor of LA's office (including the mayor). In the fourth column is the annual salary of all the employees.

NOTE: The annual salaries are already sorted in ascending order

Your job is to determine the quartiles of the annual salary and store it in a vector named salaryQuartiles

Find the Median

Using whatever method you'd like, find the median of the annual salaries. Since the dataset is 177 elements long, we know the median is the value in the middle. This is the 50% value.

Split the Set

Once you find the median value, split the data set into two separate data sets that do not include the median value. Again, use whatever method you'd like to find the median of the two data sets. This represents the 25% value (median of the lower set) and the 75% value (the median of the upper set).

Merge the Results

Store all the final values into a single vector named salaryQuartiles

NOTE: You may not use the quantiles(), prctile(), or iqr() functions