Question

Show that, if you had an income of $$\$ 20,000$$ last year and Rockefeller had an income of $$\$ 2,000,000$$, then your joint average income would be $$\$ 1,010,000$$ with a standard deviation of $$\$ 990,000$$.

Name: Problem 60, Chapter 2: Probability, Statistics, and Queuing Theory with Computer Science Applications, Second Edition (Computer Science and Scientific Computing)
Uploaded: 2023-07-31T21:45:23-08:00
Channel: Tanvi Garg
Description: Show that, if you had an income of 20,000 last year and Rockefeller had an income of 2,000,000, then your joint average income would be 1,010,000 with a standard deviation of 990,000.

   Show that, if you had an income of $$\$ 20,000$$ last year and Rockefeller had an income of $$\$ 2,000,000$$, then your joint average income would be $$\$ 1,010,000$$ with a standard deviation of $$\$ 990,000$$.

Probability, Statistics, and Queuing Theory with Computer Science Applications, Second Edition (Computer Science and Scientific Computing)

Arnold O. Allen 2nd Edition

Chapter 2, Problem 60

Instant Answer

Solved by Expert Tanvi Garg

07/31/2023

Step 1

To find the average income of two people, you add their incomes together and then divide by the number of people. In this case, the incomes are \$20,000 and \$2,000,000. So, the calculation is: \[ \text{Average Income} = \frac{\$20,000 + \$2,000,000}{2} = Show more…

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Show that, if you had an income of $$\$ 20,000$$ last year and Rockefeller had an income of $$\$ 2,000,000$$, then your joint average income would be $$\$ 1,010,000$$ with a standard deviation of $$\$ 990,000$$.

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Key Concepts

Arithmetic Mean

The arithmetic mean is the sum of all values divided by the number of values. In this context, calculating the joint average income involves adding the two incomes and dividing by two. This measure gives a central value representing the overall income level of the group.

Standard Deviation

Standard deviation quantifies the dispersion or spread of a set of data values relative to their mean. It is computed by determining each value's deviation from the mean, squaring these deviations, averaging the squared deviations, and then taking the square root of that average. In this problem, the standard deviation reflects how far each individual income is from the average income, demonstrating the variability between the two incomes.

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