Question

determining outliers – two methods
method 2
an outlier is a value located 2 or more standard deviations above, or below, the mean.
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low outlier < mean - 2 x sd
key takeaways

1. how can we determine if a value in a data set is an outlier?

• less than 1.5 x iqr below q1 or more than 1.5 x iqr above q3
• 2 or more standard deviations away from the mean

1. which summary statistics are resistant and which are nonresistant?

resistant: median, iqr
nonresistant: mean, standard deviation, range

1. which measures of center and variability are best for describing a distribution?

the following boxplot summarizes the heights of a sample of 100 trees growing on a tree farm.
tree height (inches)
emily claims that a tree height of 43 inches is an outlier for the distribution. based on the 1.5xiqr rule for outliers, is there evidence to support the claim?

Explanation:

Step1: Identify Q1, Q3 from box - plot

From the box - plot, Q1 = 32, Q3 = 36.

Step2: Calculate IQR

IQR=Q3 - Q1=36 - 32 = 4.

Step3: Calculate the upper - bound for non - outliers

The upper - bound for non - outliers is Q3+1.5×IQR. Substitute the values: 36+1.5×4=36 + 6=42.

Step4: Check if 43 is an outlier

Since 43>42, 43 is an outlier according to the 1.5×IQR rule.

Answer:

Yes, there is evidence to support the claim that a tree height of 43 inches is an outlier.