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Chapter 3: Problem 25

The mean age of six persons is 46 years. The ages of five of these six persons are \(57,39,44,51\), and 37 years, respectively. Find the age of the sixth person.

Short Answer

Expert verified
The age of the sixth person is 48 years.

Step by step solution

01

Understand the Problem

The problem is about finding the age of the sixth person. We have the mean age of six people (46 years) and the ages of five of them (57,39,44,51,37 years). We can calculate the total age of all 6 people using the mean age, then subtract the known ages to find the age of the sixth person.
02

Calculate the Total Age of all 6 people

The mean is calculated by dividing the total sum by the number of values. In this case, \(Mean = \frac{Total Sum}{Number of Values}\), or \(46 = \frac{Total Sum}{6}\). Solve this equation to find the total sum is 276 years.
03

Calculate the Age of the Sixth Person

We have the total age of all 6 people (276 years) and the sum of the ages of the five known people. Add the five known ages together to find the total so far (57+39+44+51+37 = 228 years). Subtract this from the total for all 6 people to find the age of the sixth person: \(276 - 228 = 48\) years.

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Most popular questions from this chapter

One property of the mean is that if we know the means and sample sizes of two (or more) data sets, we can calculate the combined mean of both (or all) data sets. The combined mean for two data sets is calculated by using the formula $$ \text { Combined mean }=\bar{x}=\frac{n_{1} \bar{x}_{1}+n_{2} \bar{x}_{2}}{n_{1}+n_{2}} $$ where \(n_{1}\) and \(n_{2}\) are the sample sizes of the two data sets and \(\bar{x}_{1}\) and \(\bar{x}_{2}\) are the means of the two data sets, respectively. Suppose a sample of 10 statistics books gave a mean price of \(\$ 140\) and a sample of 8 mathematics books gave a mean price of \(\$ 160\). Find the combined mean. (Hint: For this example: \(n_{1}=10, n_{2}=8, \bar{x}_{1}=\$ 140, \bar{x}_{2}=\$ 160 .\) )

Prices of cars have a distribution that is skewed to the right with outliers in the right tail. Which of the measures of center is the best to summarize this data set? Explain.

Briefly explain the empirical rule. To what kind of distribution is it applied?

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