Questions: Which of the following are resistant measures of central tendency? Select all that apply. A. Variance B. Median C. Standard Deviation D. Range E. Mean F. Interquartile Range

Solution Steps

To determine which measures of central tendency are resistant, we need to identify those that are not significantly affected by extreme values (outliers). Resistant measures include the median and the interquartile range (IQR), while non-resistant measures include the mean, variance, standard deviation, and range.

We are given a list of measures: \( \text{Variance}, \text{Median}, \text{Standard Deviation}, \text{Range}, \text{Mean}, \text{Interquartile Range} \).

Next, we classify these measures based on their resistance to outliers. The resistant measures are those that are not significantly affected by extreme values.

• The median (\( \text{Median} \)) is resistant because it represents the middle value of a dataset, which remains unchanged by outliers.
• The interquartile range (\( \text{IQR} \)) is also resistant as it measures the spread of the middle 50% of the data, ignoring extreme values.

The non-resistant measures include:

• Mean (\( \text{Mean} \))
• Variance (\( \text{Variance} \))
• Standard Deviation (\( \text{Standard Deviation} \))
• Range (\( \text{Range} \))

From our analysis, the resistant measures of central tendency are:

• \( \text{Median} \)
• \( \text{Interquartile Range} \)

Final Answer