To determine what the length of the interval that contains the middle 50% of measurements is called, let's go through the definitions of the given options:
1. The 50% percentile: This term generally refers to the median, which is the value that separates the higher half of a data sample from the lower half.
2. The tolerance interval: This is an interval within which a specified proportion of measurements in a population falls. It’s not specifically oriented towards the middle 50%.
3. The median: The median is just a single value that represents the middle of a data set, not an interval.
4. The interquartile range (IQR): The IQR is the measure of statistical dispersion, or spread, and is the length of the interval containing the middle 50% of measurements. It is calculated as the difference between the 75th percentile (Q3) and the 25th percentile (Q1).
Considering these definitions, the correct answer is:
The interquartile range
So the length of the interval that contains the middle 50% of measurements is known as the interquartile range. Therefore, the answer is:
The interquartile range.
