Which of the following are resistant measures of central​ tendency?

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Part 1

Select all that apply.

A.

Interquartile Range

B.

Median

C.

Standard Deviation

D.

Mean

E.

Range

F.

Variance

Resistant measures of central tendency are those that are not significantly affected by extreme values or outliers in a dataset. Let's analyze each option:

### Resistant Measures:
- **(B) Median:** The median is a resistant measure because it represents the middle value of a sorted dataset, making it unaffected by extreme values.
  
### Non-resistant Measures:
- **(A) Interquartile Range (IQR):** Although not a measure of central tendency but of variability, the IQR is resistant as it measures the spread of the middle 50% of the data and is unaffected by outliers.
- **(C) Standard Deviation:** Non-resistant, as it is heavily influenced by outliers.
- **(D) Mean:** The mean is non-resistant because it is affected by extreme values.
- **(E) Range:** The range is non-resistant because it considers only the highest and lowest values.
- **(F) Variance:** Variance is also non-resistant as it is influenced by outliers.

### Therefore, the correct answer is:
- **B. Median**

Would you like further details or have any questions?

### 5 Related Questions:
1. What is the difference between resistant and non-resistant measures of central tendency?
2. Why is the median preferred over the mean in skewed distributions?
3. How do outliers impact measures like the mean and standard deviation?
4. What are other resistant measures of spread besides the IQR?
5. In what situations would the mean be a more appropriate measure than the median?

### Tip:
When dealing with skewed data or outliers, consider using the median or IQR for a more accurate representation of central tendency and spread.

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

Explore which measures of central tendency are resistant to outliers in data. Understand why the median is a resistant measure while the mean and standard deviation are non-resistant. This question is suitable for Grades 10-12 students studying statistics and data analysis.

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