[Data Analysis]A data analyst creates a report that identifies the middle 50% of the collected dat a. Which of the following best describes the…

The interquartile range (IQR) is the statistical measure that represents the middle 50% of a dataset. It is calculated by subtracting the first quartile (Q1), or the 25th percentile, from the third quartile (Q3), or the 75th percentile. The range between Q1 and Q3 contains the central half of the ordered data, providing a robust measure of statistical dispersion that is not affected by outliers. This is precisely what the analyst's report identifying the middle 50% of the data describes.

B. The difference between mode and median is a measure of a distribution's skewness, not a range representing the central 50% of data points.
C. Mean variance quantifies the average squared difference from the mean, measuring the overall spread of the data, not specifically the middle 50%.
D. Skewness describes the asymmetry of a data distribution relative to its mean, not the range of the central portion of the data. ---

1. Freund, J. E., & Perles, B. M. (2007). Modern Elementary Statistics (12th ed.). Pearson Prentice Hall. In Chapter 3, "Summarizing Data: Measures of Dispersion," the interquartile range is defined as "the length of the interval that contains the middle 50 percent of the data" (p. 79).

2. Illowsky, B., & Dean, S. (2018). Introductory Statistics. OpenStax, Rice University. In Chapter 2, "Descriptive Statistics," Section 2.5, "Measures of the Center of the Data," it is stated: "The interquartile range is the range of the middle 50 percent of the data values; the IQR is found by subtracting the first quartile from the third quartile" (p. 93).

3. MIT OpenCourseWare. (2014). 18.05 Introduction to Probability and Statistics, Spring 2014. Reading 1: Introduction to Statistics. Section 6.2, "Quartiles and the Interquartile Range (IQR)," defines the IQR as Q3 - Q1 and explains that "The interval [Q1, Q3] contains the middle 50% of the data."