The ________ ________ is the range of the middle 50% of the observations in a data set.

Verified step by step guidance

1. Identify the term that describes the range of the middle 50% of the observations in a data set. This term is a measure of statistical dispersion.
2. Recall that the middle 50% of data corresponds to the data between the 25th percentile (Q1) and the 75th percentile (Q3).
3. Understand that the range between these two quartiles is called the interquartile range (IQR).
4. Express the interquartile range mathematically as \(\text{IQR} = Q_3 - Q_1\), where \(Q_3\) is the third quartile and \(Q_1\) is the first quartile.
5. Conclude that the phrase to fill in the blanks is 'interquartile range', which represents the spread of the middle 50% of the data.

Key Concepts

Interquartile Range (IQR)

The interquartile range (IQR) measures the spread of the middle 50% of data points in a dataset. It is calculated as the difference between the third quartile (Q3) and the first quartile (Q1), representing the range where the central half of the observations lie.

Quartiles

Quartiles divide a dataset into four equal parts after sorting the data. The first quartile (Q1) marks the 25th percentile, and the third quartile (Q3) marks the 75th percentile, helping to identify the spread and center of the data.

Data Distribution and Spread

Understanding data distribution involves analyzing how data points are spread across values. Measures like range, variance, and IQR describe this spread, with IQR focusing on the central portion, reducing the effect of outliers.