Concept explainers
To calculate: The mean deviation and the standard deviation of
Answer to Problem 15E
The standard deviation is
Explanation of Solution
Given information:
Formula used:
A measure of variability associated with the arithmetic mean is the standard deviation.
The arithmetic mean of the absolute values of the deviations from the mean of a set of data is called the mean deviation.
Formula of Mean
Calculation:
Consider the data ,
So,
The mean of the data is
Therefore , the standard deviation is −
369 | 403.5 | ||
376 | 403.5 | ||
381 | 403.5 | ||
385 | 403.5 | ||
392 | 403.5 | ||
398 | 403.5 | ||
402 | 403.5 | ||
406 | 403.5 | ||
413 | 403.5 | ||
420 | 403.5 | ||
446 | 403.5 | ||
454 | 403.5 | ||
The mean deviation is −
369 | 403.5 | |
376 | 403.5 | |
381 | 403.5 | |
385 | 403.5 | |
392 | 403.5 | |
398 | 403.5 | |
402 | 403.5 | |
406 | 403.5 | |
413 | 403.5 | |
420 | 403.5 | |
446 | 403.5 | |
454 | 403.5 | |
Hence, the standard deviation is
Chapter 14 Solutions
Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
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