Which of the following are resistant measures of centraltendency? Select all that apply. A. Standard Deviation B. Range C. Interquartile Range D. Variance E. Mean F. Median
The Correct Answer and Explanation is :
The resistant measures of central tendency are those that are not heavily influenced by extreme values, or outliers, in the dataset. To answer this question, let’s go through each of the options:
A. Standard Deviation
The standard deviation is not resistant. It is heavily affected by outliers because it is based on squared deviations from the mean. When extreme values exist in a dataset, they increase the variance, and thus the standard deviation, making it sensitive to outliers.
B. Range
The range is not resistant. It is calculated by subtracting the smallest value from the largest value in the dataset, meaning it is highly affected by outliers or extreme values. If there is an unusually high or low value, the range will be disproportionately large.
C. Interquartile Range (IQR)
The interquartile range (IQR) is resistant. The IQR measures the range between the first quartile (Q1) and the third quartile (Q3), which are the 25th and 75th percentiles of the data. It focuses on the middle 50% of the data and is not significantly influenced by extreme values or outliers.
D. Variance
Variance, like the standard deviation, is not resistant. It is calculated based on the squared differences from the mean, meaning it too is sensitive to outliers. Extreme values cause larger squared deviations, thereby increasing the variance.
E. Mean
The mean is not resistant. The mean is calculated by summing all the values in the dataset and dividing by the number of values. Outliers can heavily skew the mean, making it unrepresentative of the majority of data points in a dataset with extreme values.
F. Median
The median is resistant. The median is the middle value of a dataset when arranged in order. It does not change significantly if extreme values are added, as long as they don’t affect the central position. This makes the median a resistant measure of central tendency.
Correct answers:
- C. Interquartile Range (IQR)
- F. Median
These two measures are resistant because they are less affected by outliers and extreme values. The IQR only considers the middle 50% of the data, and the median is the middle value, unaffected by the extreme values at either end of the dataset.