Answered: If the mean median, and mode are all…

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 the mean median, and mode are all computed for a distribution of scores, which of the following statements cannot be true?

A. No one had a score equal to the mode

B. No one had a score equal to the mean

C. No one had a score equal to the median

D. All of the other three statements cannot be true

Definition Definition Measure of central tendency that is the value that occurs most frequently in a data set. A data set may have more than one mode if multiple categories repeat an equal number of times. For example, in a data set with five item—3, 5, 5, 29, 473—the mode is 5 because it occurs twice and no other value occurs more than once. On a histogram or bar chart, the element with the highest bar represents the mode. Therefore, the mode is sometimes considered the most popular option. The mode is useful for nominal or categorical data (e.g., the most common color car that users purchase), but it is problematic for continuous data because it is more likely not to have any value that is more frequent than the other.

Expert Solution

Step 1

Mean:

Mean represents the average of the sample.

That is,

M=∑X/n

Median:

Arrange the individual scores in ascending order and check if N is even or odd.

N is even: Median is the average of middle two scores.

N is odd: Median is the middle value

Mode:

The score or category that has the greatest frequency is said to be mode.

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