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Chapter 3: Problem 28

The mean 2011 income for five families was \(\$ 99.520 .\) What was the total 2011 income of these five families?

Short Answer

Expert verified
The total 2011 income of the five families was \$497,600.

Step by step solution

01

Understand the Problem Statement

This problem is asking to find the total income of five families given their mean income. The mean or average income is obtained when the total income is divided by the number of families. In this case, we already know the mean income, which is \$99,520, and the number of families, which is 5.
02

Apply the Formula of Mean

The formula for the mean is \( Mean = \frac{Total\;Income}{No.\;of\;Families} \). However, we want to find out the total income, which will be \( Total\;Income = Mean \times No.\;of\;Families \)
03

Calculate the Total Income

Substitute the given values into the formula: \( Total\;Income = \$99,520 \times 5 \). Thus, the total income for the five families in 2011 was \$497,600.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Income Calculation
Income calculation is a pivotal part of understanding personal and economic finance. In many instances, we need to calculate the total income of a group, given an average income, to assess financial potential or requirements. Mean income is the average income calculated by dividing the total income by the number of entities involved.
For example, if we have the mean income and the number involved, the total income can simply be calculated using the formula:
  • Total Income = Mean Income 脳 Number of Entities
Essential to income calculation is understanding what 'mean' refers to and how it assists in determining collective financial figures.
Basic Statistics
Basic statistics involves understanding and analyzing data to make informed decisions. The mean or average is one of the most fundamental concepts in statistics. It provides a simple summary of a data set by dividing the sum of all data points by the number of data points.
In everyday problems, like calculating total income, the mean becomes a useful tool. By knowing the mean and the number of data points, we can reverse calculate the total sum. This is a fundamental use of statistics in solving practical problems.
  • Mean = Total Sum / Number of Data Points
  • Or equivalently: Total Sum = Mean 脳 Number of Data Points
Understanding these basic equations builds a strong foundation for further statistical study and practical application.
Problem Solving Steps
Problem-solving often involves breaking down complex problems into simpler steps. Here's a straightforward approach applied in our example:
  • Step 1: Understand the Problem - Clearly grasp what is being asked. Know your facts: the mean income and number of families in our case.
  • Step 2: Use the Right Formula - Identify what formula you need. For calculating total income from mean, use: Total Income = Mean 脳 Number of Families.
  • Step 3: Perform the Calculation - Substitute the known values into your formula. Calculate: 99,520 脳 5.
This structured approach prevents errors and simplifies the process of finding solutions, ensuring you arrive at the correct answer efficiently.

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Most popular questions from this chapter

Refer to Exercise \(2.94\), which listed the alcohol content by volume for each of the 13 varieties of beer produced by Sierra Nevada Brewery. Those data are reproduced here: \(\begin{array}{llllllllll}4.4 & 5.0 & 5.0 & 5.6 & 5.6 & 5.8 & 5.9 & 5.9 & 6.7 & 6.8\end{array}\) \(\begin{array}{lll}6.9 & 7.0 & 9.6\end{array}\) Calculate the range, variance, and standard deviation.

The following stem-and-leaf diagram gives the distances (in thousands of miles) driven during the past year by a sample of drivers in a city. $$ \begin{array}{l|llllll} 0 & 3 & 6 & 9 & & & \\ 1 & 2 & 8 & 5 & 1 & 0 & 5 \\ 2 & 5 & 1 & 6 & & & \\ 3 & 8 & & & & & \\ 4 & 1 & & & & & \\ 5 & & & & & & \\ 6 & 2 & & & & \end{array} $$ a. Compute the sample mean, median, and mode for the data on distances driven. b. Compute the range, variance, and standard deviation for these data. c. Compute the first and third quartiles. d. Compute the interquartile range. Describe what properties the interquartile range has. When would the IQR be preferable to using the standard deviation when measuring variation?

According to www.money-zine.com, the average FICO score in the United States was around 692 in December \(2011 .\) Suppose the following data represent the credit scores of 22 randomly selected loan applicants. \(\begin{array}{lllllllllll}494 & 728 & 468 & 533 & 747 & 639 & 430 & 690 & 604 & 422 & 356 \\ 805 & 749 & 600 & 797 & 702 & 628 & 625 & 617 & 647 & 772 & 572\end{array}\) a. Calculate the values of the three quartiles and the interquartile range. Where does the value 617 fall in relation to these quartiles? b. Find the approximate value of the 30 th percentile. Give a brief interpretation of this percentile. c. Calculate the percentile rank of 533 . Give a brief interpretation of this percentile rank.

The annual earnings of all employees with CPA certification and 6 years of experience and working for large firms have a bell-shaped distribution with a mean of \(\$ 134,000\) and a standard deviation of \(\$ 12,000 .\) a. Using the empirical rule, find the percentage of all such employees whose annual eamings are between i. \(\$ 98,000\) and \(\$ 170,000\) ii. \(\$ 110,000\) and \(\$ 158,000\) *b. Using the empirical rule, find the interval that contains the annual earnings of \(68 \%\) of all such employees.

Prepare a box-and-whisker plot for the following data: \(\begin{array}{llllllll}36 & 43 & 28 & 52 & 41 & 59 & 47 & 61 \\ 24 & 55 & 63 & 73 & 32 & 25 & 35 & 49 \\ 31 & 22 & 61 & 42 & 58 & 65 & 98 & 34\end{array}\) Does this data set contain any outliers?
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