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 [tex]\displaystyle z=\frac{x_i-\mu}{\sigma}[/tex].
Substituting [tex]x_i=21, \mu = 4.428571429, \sigma=4.4336376551476[/tex], we get [tex]z\approx 3.73[/tex].
To determine if a value is an outlier, we use IQR, or Interquartile Range. If a value is lower than [tex]Q1-1.5\times IQR[/tex] or higher than [tex]Q3+1.5\times IQR[/tex], 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 [tex]Q3+1.5\times IQR=6.5+1.5\cdot 4.5=13.25[/tex]. Any values above 13.25 are considered high outliers. Therefore, the maximum value of 21 is a high outlier.
