/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 7 For Exercises 7 through \(12,\) ... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

For Exercises 7 through \(12,\) rank each set of data. $$ 25,68,36,63,36,74,39 $$

Short Answer

Expert verified
The ranked data set is 25, 36, 36, 39, 63, 68, 74.

Step by step solution

01

Understand the Problem

We need to rank a set of numbers, which means rearranging the numbers from the smallest to the largest.
02

Identify the Numbers

List the numbers we need to rank. The numbers are: 25, 68, 36, 63, 36, 74, 39.
03

Arrange the Numbers in Ascending Order

Start listing the numbers from the smallest to the largest: 25, 36, 36, 39, 63, 68, 74.

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Key Concepts

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

Data Ranking
Data ranking is a crucial part of analyzing numerical information. It involves arranging numbers or values in a specific order to draw meaningful conclusions. When you rank data, you align numbers from the lowest to the highest, or vice versa, based on a chosen criterion.
  • This helps easily identify trends or outliers.
  • It can be used to determine relative positions and to compare different data points.
For example, in a list like 25, 68, 36, 63, 36, 74, and 39, ranking would involve ordering these numbers so you can immediately see how each number compares to the others. Ranking is handy when identifying the minimum or maximum value in a dataset and understanding the distribution of numbers. It serves as a foundational technique in statistical analysis and is often a preliminary step before more complex statistical tasks.
Ordering Data
Ordering data refers to sorting a list of numbers or values in a sequence. Usually, this is done from the smallest to the largest number, which is regarded as ascending order. Conversely, ordering from largest to smallest is called descending order.
  • Ordering data helps in visualizing datasets clearly.
  • It facilitates easier data interpretation and analysis.
To order the data set 25, 68, 36, 63, 36, 74, and 39, you start by scanning for the smallest number, which is 25, and proceed placing the next smallest numbers sequentially until you reach the largest number, 74. This gives us a new ordered list: 25, 36, 36, 39, 63, 68, 74. By organizing data purposefully, you can detect patterns, locate central tendencies, and address outliers effectively. These are essential steps in many statistical processes and analyses.
Elementary Statistics
Elementary statistics involve basic statistical concepts used to describe and summarize data. This includes measures of central tendency like mean, median, and mode, as well as analysis techniques like data ranking and ordering.
  • Elementary statistics provide tools to summarize large data sets with simple figures.
  • They form the basis for more advanced statistical practices.
By employing methods like ranking and ordering, you can improve your understanding of data distribution and typical values within a dataset. This is valuable in many fields, such as economics, biology, and social sciences. Elementary statistics not only help in simplifying complex data, but they also enable effective communication of initial findings, making data manageable and meaning more accessible to those without a deep statistical background.

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Most popular questions from this chapter

What population parameter can be tested with the sign test?

List the advantages of nonparametric statistics.

The confidence interval for the median of a set of values less than or equal to 25 in number can be found by ordering the data from smallest to largest, finding the median, and using Table J. For example, to find the \(95 \%\) confidence interval of the true median for \(17,19,3,8,10,15,1,23,2,12,\) order the data: $$ 1,2,3,8,10,12,15,17,19,23 $$ From Table \(\mathrm{J}\), select \(n=10\) and \(\alpha=0.05,\) and find the critical value. Use the two-tailed row. In this case, the critical value is \(1 .\) Add 1 to this value to get \(2 .\) In the ordered list, count from the left two numbers and from the right two numbers, and use these numbers to get the confidence interval, as shown: $$ \begin{array}{l}{1,2,3,8,10,12,15,17,19,23} \\ {2 \leq \mathrm{MD} \leq 19}\end{array} $$ Always add 1 to the number obtained from the table before counting. For example, if the critical value is \(3,\) then count 4 values from the left and right. For Exercises 21 through 25 , find the confidence interval of the median, indicated in parentheses, for each set of data. $$ \begin{array}{l}{12,15,18,14,17,19,25,32,16,47,14,23,27,42,33,} \\\ {35,39,41,21,19(95 \%)}\end{array} $$

Explain what is meant by the efficiency of a nonparametric test.

For Exercises 5 through \(14,\) perform these steps. a. Find the Spearman rank correlation coefficient. b. State the hypotheses. c. Find the critical value. Use \(\alpha=0.05\) d. Make the decision. e. Summarize the results. Use the traditional method of hypothesis testing unless otherwise specified. Subway and Commuter Rail Passengers Six cities are randomly selected, and the number of daily passenger trips (in thousands) for subways and commuter rail service is obtained. At \(\alpha=0.05,\) is there a relationship between the variables? Suggest one reason why the transportation authority might use the results of this study. $$ \begin{array}{c|cccccc}{\text { City }} & {1} & {2} & {3} & {4} & {5} & {6} \\\ \hline \text { Subway } & {845} & {494} & {425} & {313} & {108} & {41} \\\ \hline \text { Rail } & {39} & {291} & {142} & {103} & {33} & {38}\end{array} $$

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