In set of data with highly variable values,the best measure of central tendency is
**Core Concept**
The question is testing the student's understanding of measures of central tendency in a dataset with highly variable values. In statistics, measures of central tendency (mean, median, mode) help describe the central or typical value of a dataset. However, when the dataset has highly variable values, the mean is often skewed, and the median is a more appropriate measure of central tendency.
**Why the Correct Answer is Right**
The median is the middle value of a dataset when it is ordered from smallest to largest. In a dataset with highly variable values, the median is less affected by extreme values (outliers) than the mean. This is because the mean is calculated by summing all the values and dividing by the number of values, which can be skewed by a single outlier. In contrast, the median is simply the middle value, which is more resistant to the influence of outliers.
**Why Each Wrong Option is Incorrect**
* **Option A:** The mode is the most frequently occurring value in a dataset. However, the mode is not necessarily a good measure of central tendency, especially in datasets with highly variable values, as it may not accurately represent the typical value.
* **Option B:** The range is a measure of variability, not a measure of central tendency. It is the difference between the highest and lowest values in a dataset.
* **Option D:** The standard deviation is a measure of variability, not a measure of central tendency. It is a statistical tool used to quantify the amount of variation or dispersion from the mean.
**Clinical Pearl / High-Yield Fact**
When analyzing a dataset with highly variable values, always consider using the median as a measure of central tendency to avoid being skewed by outliers.
**Correct Answer:** C. Median