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Chapter 9: Problem 478

A family had eight children. The ages were \(9,11,8,15,14\), \(12,17,14\) (a) Find the measures of central tendency for the data. (b) Find the range of the data.

Short Answer

Expert verified
(a) Mean: \(12.5\) years old, Median: \(13\) years old, Mode: \(14\) years old. (b) Range: \(9\).

Step by step solution

01

Arrange the data in ascending order

Firstly, let's arrange the given ages in ascending order: 8, 9, 11, 12, 14, 14, 15, 17.
02

Calculate the mean (average) age

To find the mean, we need to add the ages together and then divide by the total number of children (8). Using the ordered data: \[Mean = \frac{8 + 9 + 11 + 12 + 14 + 14 + 15 + 17}{8} = \frac{100}{8} = 12.5\]
03

Calculate the median age

To find the median, we need to identify the middle value(s) in our ordered data. Since there are eight children (an even number), the median will be the average of the two middle values. In this case, the middle values are 12 and 14, so the median is: \[Median = \frac{12 + 14}{2} = 13\]
04

Calculate the mode age

The mode is the most frequent age in the dataset. In our ordered data, we can see that the age 14 occurs twice, which is the most frequent. Thus, the mode is 14.
05

Calculate the range of the data

To find the range of the data, we need to subtract the lowest age from the highest age in the dataset. Using the ordered data: \[Range = 17 - 8 = 9\] In conclusion: (a) The measures of central tendency for the data are: - Mean: 12.5 years old - Median: 13 years old - Mode: 14 years old (b) The range of the data is 9.

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Most popular questions from this chapter

Suppose that you want to decide which of two equally-priced brands of light bulbs lasts longer. You choose a random sample of 100 bulbs of each brand and find that brand \(\mathrm{A}\) has sample mean of 1180 hours and sample standard deviation of 120 hours, and that brand \(\mathrm{B}\) has sample mean of 1160 hours and sample standard deviation of 40 hours. What decision should you make at the \(5 \%\) significance level?

Out of a group of 10,000 degree candidates of The University of North Carolina at Chapel Hill, a random sample of 400 showed that 20 per cent of the students have an earning potential exceeding \(\$ 30,000\) annually. Establish a \(.95\) confidence- interval estimate of the number of students with a \(\$ 30,000\) plus earning potential.

A highly specialized industry builds one device each month. The total monthly demand is a random variable with the following distribution. $$ \begin{array}{|l|l|l|l|l|} \hline \text { Demand } & 0 & 1 & 2 & 3 \\ \hline \mathrm{P}(\mathrm{D}) & 1 / 9 & 6 / 9 & 1 / 9 & 1 / 9 \\ \hline \end{array} $$ When the inventory level reaches 3, production is stopped until the inventory drops to 2 . Let the states of the system be the inventory level. The transition matrix is found to be \(\begin{array}{rlllll} & & 0 & 1 & 2 & 3 \mid \\\ & 0 & 8 / 9 & 1 / 9 & 0 & 0 \\ & 11 & 2 / 9 & 6 / 9 & 1 / 9 & 0 \\\ \mathrm{P}= & 12 & 1 / 9 & 1 / 9 & 6 / 9 & 1 / 9 \\ & 13 & 1 / 9 & 1 / 9 & 6 / 9 & 1 / 9\end{array}\) Assuming the industry starts with zero inventory find the transition matrix as \(\mathrm{n} \rightarrow \infty\)

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