If a histogram is skewed with a long left tail, which of the following must be correct? The sample mean is larger than the sample median. The sample mean is smaller than the sample median. Some data points should be classified as outliers.

If a histogram is skewed with a long left tail, which of the following must be correct? The sample mean is larger than the sample median. The sample mean is smaller than the sample median. Some data points should be classified as outliers.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

If a histogram is skewed with a long left tail, which of the following must be correct?

The sample mean is larger than the sample median.
The sample mean is smaller than the sample median.
Some data points should be classified as outliers.

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

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