Question

These are the two I need help with:

Answer 1

Answer:

Z-score = 3.73

Yes, the maximum value (21) in this data set is a high outlier.

Step-by-step explanation:

I'll solve for what you haven't done yet, z-score and whether or not the maximum is an outlier.

Z-score tells us how many standard deviations a value is above or below the mean. The formula for z-score is $\displaystyle z=\frac{x_i-\mu}{\sigma}$.

Substituting $x_i=21, \mu = 4.428571429, \sigma=4.4336376551476$, we get $z\approx 3.73$.

To determine if a value is an outlier, we use IQR, or Interquartile Range. If a value is lower than $Q1-1.5\times IQR$ or higher than $Q3+1.5\times IQR$, then we say it is an outlier.

With the value of 21, clearly we are only worried about it being a high outlier. Q1 is the median of the first half of the data and Q3 is the median of the second half. In this case, Q1 is 2 and Q3 is 6.5. IQR is equal to Q3-Q1, or 4.5 in this case.

Therefore, the higher limit for outliers is $Q3+1.5\times IQR=6.5+1.5\cdot 4.5=13.25$. Any values above 13.25 are considered high outliers. Therefore, the maximum value of 21 is a high outlier.