You will need the SaratogaHouses data set, which is in the mosaicData package. This is done within the program R.

1) Measuring skew

A variable is called skewed if it has a long tail or outliers on one side. (For some visual examples, see http://www.statisticshowto.com/probability-and-statistics/skewed-distribution/.) One numerical measure of skewness is Pearson's median skewness coefficient:

$\frac{3*(mean(x) - median(x))}{sd(x)}$

(Recall that sd stands for standard deviation. Notice that a coefficient > 0 indicates right skewness, and a coefficient < 0 indicates left skewness.)

1a.

Write a function, `pearson_skew`, which computes Pearson's median skewness coefficient for a vector x. (For now, you may assume that x contains only numeric values and no NAs.)

Use your function to compute Pearson's median skewness coefficient for the vector `example_1a`:

example_1a = c( 1, 1, 2, 10 )

1b.

Modify function so it accepts additional arguments (such as na.rm = TRUE) and passes them to the functions it calls.

Use your function to compute Pearson's median skewness coefficient for the vector `example_1b`:

example_1b = c( 1, 2, 5, NA, 9 )

```

1c.

Modify your function so it returns two pieces of output: The skewness coefficient, and the length of the vector.

Run the following code (without changes) to create the vector `example_1c`.Then find what `pearson_skew` returns when applied to this vector.

set.seed(999)

example_1c = rexp(floor(runif(1, 101, 199)), 2)