Answered: Eight people took a test in which one…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Eight people took a test in which one can score only 1, 2, or 3.
(a) You know that exactly two people scored 1 and that the distribu-
tion is summetric about the mean. What is that variance of the set
of scores?
(b) Let the variance of the set be 1. List the eight scores.
(c) Given that the mean of the scores is 3, what is the standard devia-
tion of the set of scores?[1, 1.1.131
10. The treasury department is considering several schemes for revising its
salary and employment policies for government workers.
The following three schemes are suggested. Determine, in each case,
how the suggested revision would affect each of the following mea-
sures:
(a) Each employee will get a raise of $125 per month.
(b) The salaries will be increased by 15% across the board.
(c) The number of employees at each salary level will be decreased
to 90% of their original number.
1. The mean monthly salary in dollars.
i. The variance of the monthly salaries.
ill. The standard deviation of the monthly salaries.
iv. The median monthly salary.
v. The modal monthly salary.[1, 1.1.15]

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.

Expert Solution

Step 1

Hello! As you have posted 2 different questions, we are answering the first question. In case you require the unanswered question also, kindly re-post them as separate question.

From the given information,

Eight people took a test in which one can score only 1, 2, or 3.

You know that exactly two people scored 1 and that the distribution is symmetric about the mean.

Since the distribution is symmetric, two scores must be 3.

Then, the remaining people are 4. These 4 people takes the scores 2.

Hence, the scores are 1, 1, 2, 2, 2, 2, 3, 3.

Mean:

$M e a n = \frac{s u m o f s c o r e s}{N u m b e r o f s c o r e s} = \frac{1 + 1 + 2 + 2 + 2 + 2 + 3 + 3}{8} = 2$

Variance:

$V a r i a n c e = \frac{\sum_{} {(s c o r e - m e a n)}^{2}}{n u m b e r o f s c o r e s - 1} = \frac{{(1 - 2)}^{2} + {(1 - 2)}^{2} + {(2 - 2)}^{2} + {(2 - 2)}^{2} + {(2 - 2)}^{2} + {(2 - 2)}^{2} + {(3 - 2)}^{2} + {(3 - 2)}^{2}}{8 - 1} = 0.5714$

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Follow-up Questions

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Follow-up Question

10. The treasury department is considering several schemes for revising its
salary and employment policies for government workers.
The following three schemes are suggested. Determine, in each case,
how the suggested revision would affect each of the following mea-
sures:
(a) Each employee will get a raise of $125 per month.
(b) The salaries will be increased by 15% across the board.
(c) The number of employees at each salary level will be decreased
to 90% of their original number.
1. The mean monthly salary in dollars.
i. The variance of the monthly salaries.
ill. The standard deviation of the monthly salaries.
iv. The median monthly salary.
v. The modal monthly salary.[1, 1.1.15]