Question

14.1 health care
the histogram and box plot show the average amount of money, in thousands of dollars, each person in the country (per capita spending) for health care in 34 countries.
per capita health spending by country (thousands of dollars)

1. one value in the set is an outlier. which one is it? what is its approximate value?
2. by one rule for deciding, a value is an outlier if it is more than 1.5 times the iqr greater than q3. show on the box plot whether or not your value meets this definition of outlier

Explanation:

Step1: Identify outlier from histogram

The value far from the main - cluster is around 10.

Step2: Recall outlier rule

The inter - quartile range (IQR) rule for outliers is \(Q3 + 1.5\times IQR\). First, we need to find \(Q1\), \(Q3\) and \(IQR\) from the box - plot.

Step3: Estimate quartiles from box - plot

The box in the box - plot represents the inter - quartile range. The left edge of the box is \(Q1\) (around 2.5), the right edge of the box is \(Q3\) (around 5). So \(IQR=Q3 - Q1=5 - 2.5 = 2.5\).

Step4: Calculate upper bound for non - outliers

The upper bound for non - outliers is \(Q3+1.5\times IQR=5 + 1.5\times2.5=5 + 3.75 = 8.75\).

Step5: Check the outlier value

The value around 10 is greater than 8.75, so it is an outlier.

Answer:

1. The outlier is the value around 10 thousand dollars.
2. From the box - plot, \(Q1\approx2.5\), \(Q3\approx5\), \(IQR = Q3 - Q1=2.5\). The upper bound for non - outliers is \(Q3 + 1.5\times IQR=5+1.5\times2.5 = 8.75\). Since 10>8.75, the value 10 meets the definition of an outlier.