Answered: (a) Find the mean u and the standard…

(a) Find the mean u and the standard deviation o for the collection of N = 8 stocks. (b) Find the sample mean i and sample standard deviation s of the random sample of stocks.

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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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

(a) Find the mean u and the standard deviation o for the collection
of N = 8 stocks.
(b) Find the sample mean i and sample standard deviation s of the
random sample of stocks.

Expert Solution

Step 1

(a)

The mean for the collection of $N = 8$ stocks is,

$\begin{array}{rcl} μ & = & \frac{\sum_{i = 1}^{N} x_{i}}{N} \\ = & \frac{5 + 3 + 6 + 8 + 4 + 7 + 10 + 5}{8} \\ = & \frac{48}{8} \\ = & 6 \end{array}$

Thus, the mean for the collection of $N = 8$ stocks is $6.

The standard deviation for the collection of $N = 8$ stocks is,

$\begin{array}{rcl} σ & = & \sqrt{\frac{\sum_{i = 1}^{N} (x_{i} - μ)}{N}} \\ = & \sqrt{\frac{{(5 - 6)}^{2} + {(3 - 6)}^{2} + {(6 - 6)}^{2} + {(8 - 6)}^{2} + {(4 - 6)}^{2} + {(7 - 6)}^{2} + {(10 - 6)}^{2} + {(5 - 6)}^{2}}{8}} \\ = & \sqrt{\frac{1 + 9 + 0 + 4 + 4 + 1 + 16 + 1}{8}} \\ = & \sqrt{\frac{36}{8}} \\ = & \sqrt{4.5} \\ = & 2.1213 \end{array}$

Thus, the standard deviation for the collection of $N = 8$ stocks is $2.1213.

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