Let's analyze each given option to determine the correct answer regarding the Range and Interquartile Range (IQR) of a dataset.
### Option A: "Both are considering only the middle 50% of the data."
- Range: The range of a data set is calculated as the difference between the maximum and minimum values. It considers the extreme ends of the data rather than the middle.
- Interquartile Range (IQR): The IQR is calculated as the difference between the third quartile (Q3) and the first quartile (Q1), representing the middle 50% of the data.
While the IQR only considers the middle 50% of the data, the range does not.
Thus, Option A is not true.
### Option B: "Both are affected by extreme values in the data."
- Range: Being the difference between the maximum and minimum values, the range is highly affected by extreme values (outliers).
- Interquartile Range (IQR): The IQR is a measure of statistical dispersion between the third and first quartiles. It is not affected by extreme values because it focuses on the central 50% of the data.
While the range is affected by extreme values, the IQR is not.
Thus, Option B is not true.
### Option C: "Both are measures of variation of the data."
- Range: As the difference between the maximum and minimum values, the range measures the complete spread of the data, which is a form of variation.
- Interquartile Range (IQR): By measuring the spread of the middle 50% of the data, the IQR also indicates how the data varies around the median. It is another form of measuring variation.
Both the range and the IQR are used to describe how data points are spread out, making them measures of variation.
Therefore, Option C is true.
### Option D: "Both are measures of the variability of each item in the data."
- Range: The range provides a single value that shows the overall spread of the data but does not give information about the variability of each individual data point.
- Interquartile Range (IQR): Similarly, the IQR indicates the spread of the middle 50% but does not describe the variability of each individual data point.
Neither the range nor the IQR provides information about the variability of each specific item in the dataset.
Therefore, Option D is not true.
Given this detailed analysis, the true statement regarding the Range and Interquartile Range of a given data is:
Option C: Both are measures of variation of the data.
