/*! 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 8 Rank each set of data. $$ 88... [FREE SOLUTION] | 91影视

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Chapter 13: Problem 8

Rank each set of data. $$ 88,465,587,182,243 $$

Short Answer

Expert verified
Ranks are: 1 (88), 2 (182), 3 (243), 4 (465), 5 (587).

Step by step solution

01

Identify the Dataset

List out all the numbers that are part of the given dataset: 88, 465, 587, 182, and 243.
02

Understand 'Ranking' in Context

Ranking requires ordering a set of numbers from the smallest to the largest. The position of each number in this order is its rank.
03

Sort the Dataset

Order the numbers from the smallest to the largest: 88, 182, 243, 465, 587.
04

Assign Ranks

Assign ranks based on the ordered list: - 88 is rank 1 - 182 is rank 2 - 243 is rank 3 - 465 is rank 4 - 587 is rank 5
05

Verify the Ranks

Check that each number is correctly ordered and each has a unique rank from 1 to 5.

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Key Concepts

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

Ordering Numbers
Ordering numbers is a fundamental part of ranking any dataset. It involves arranging numbers in a sequence based on certain rules, most commonly from the smallest to the largest. This process is essential in various fields such as mathematics, statistics, and daily life scenarios where comparisons are necessary.
To begin ordering numbers, one should first identify and list all the numbers in the dataset. In our example, the numbers are 88, 465, 587, 182, and 243.
  • Identify the smallest number and start the sequence with it: 88.
  • Continue selecting the next smallest number until all numbers are placed in order: 88, 182, 243, 465, 587.
Ordering numbers allows us to see patterns, trends, and outliers within a data set. This basic skill enables further analysis like ranking, which helps provide a clear picture of the relative positions of data points.
Rank Assignment
Rank assignment follows after ordering the data in sequence. It involves assigning a numerical position, known as a rank, to each number in the ordered series. This process helps in comparing different values and assessing their relative standings.
Once you have a sorted list, assigning ranks is straightforward:
  • Start with the smallest number and assign it the first rank.
  • Continue with the next smallest number in the sequence and assign it the subsequent rank, and so on.
In our dataset, after ordering, we assign ranks as follows:
  • 88 receives rank 1
  • 182 receives rank 2
  • 243 receives rank 3
  • 465 receives rank 4
  • 587 receives rank 5
Each number has a unique rank, allowing clear comparison among the data points. This method is vital for identifying hierarchies, making decisions based on importance, or simply understanding the dataset better.
Data Analysis
Data analysis involves examining, cleaning, transforming, and modeling data to discover useful information and support decision-making. Ranking is one of the many techniques used in data analysis to extract meaningful insights from a dataset.
By ranking numbers, we can:
  • Easily identify the smallest and largest values.
  • Understand the relative positions and differences between numbers.
  • Spot trends and anomalies within the dataset.
For example, in business, ranking sales data helps identify top-performing products. In academics, ranking scores can highlight the top-performing students. In general, ranking is a starting point for more complex data analysis techniques, assisting researchers and analysts in making informed decisions based on statistical evidence.

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Most popular questions from this chapter

Use the Kruskal-Wallis test and perform these steps. a. State the hypotheses and identify the claim. b. Find the critical value. c. Compute the test value. d. Make the decision. e. Summarize the results. Use the traditional method of hypothesis testing unless otherwise specified. Number of Crimes per Week In a large city, the number of crimes per week in five precincts is recorded for five randomly selected weeks. The data are shown here. At \(\alpha=0.01\), is there a difference in the number of crimes? $$ \begin{array}{rcccc} \text { Precinct } 1 & \text { Precinct } 2 & \text { Precinct } 3 & \text { Precinct } 4 & \text { Precinct } 5 \\ \hline 105 & 87 & 74 & 56 & 103 \\ 108 & 86 & 83 & 43 & 98 \\ 99 & 91 & 78 & 52 & 94 \\ 97 & 93 & 74 & 58 & 89 \\ 92 & 82 & 60 & 62 & 88 \end{array} $$

Test the hypothesis that the randomly selected assessed values have changed between 2010 and 2014 . Use \(\alpha=0.05 .\) Do you think land values in a large city would be normally distributed? $$ \begin{array}{l|ccccccccccc} \text { Ward } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } & \text { G } & \text { H } & \text { I } & \text { J } & \text { K } \\ \hline \mathbf{2 0 1 0} & 184 & 414 & 22 & 99 & 116 & 49 & 24 & 50 & 282 & 25 & 141 \\ \hline \mathbf{2 0 1 4} & 161 & 382 & 22 & 190 & 120 & 52 & 28 & 50 & 297 & 40 & 148 \end{array} $$

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. $$ \begin{array}{l|rrrrrr} \text { City } & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline \text { Subway } & 845 & 494 & 425 & 313 & 108 & 41 \\ \hline \text { Rail } & 39 & 291 & 142 & 103 & 33 & 38 \end{array} $$

When \(n \geq 30,\) the formula \(r=\frac{\pm z}{\sqrt{n-1}}\) can be used to find the critical values for the rank correlation coefficient. For example, if \(n=40\) and \(\alpha=0.05\) for a two-tailed test, $$ r=\frac{\pm 1.96}{\sqrt{40-1}}=\pm 0.314 $$ Hence, any \(r_{s}\) greater than or equal to +0.314 or less than or equal to -0.314 is significant. Find the critical \(r\) value for each (assume that the test is two-tailed). $$ n=60, \alpha=0.10 $$

Gender of Patients at a Medical Center The gender of the patients at a medical center is recorded. Test the claim at \(\alpha=0.05\) that they are admitted at random. $$ \begin{array}{llllllllll} \mathrm{F} & \mathrm{F} & \mathrm{M} & \mathrm{M} & \mathrm{M} & \mathrm{M} & \mathrm{M} & \mathrm{F} & \mathrm{F} & \mathrm{F} \\ \mathrm{M} & \mathrm{M} & \mathrm{M} & \mathrm{M} & \mathrm{M} & \mathrm{M} & \mathrm{F} & \mathrm{M} & \mathrm{M} & \mathrm{F} \\ \mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{M} & \mathrm{M} & \mathrm{M} & \mathrm{F} & \mathrm{M} & \mathrm{F} & \mathrm{M} \\ \mathrm{M} & \mathrm{M} & \mathrm{M} & \mathrm{M} & \mathrm{M} & \mathrm{F} & \mathrm{M} & \mathrm{M} & \mathrm{F} & \mathrm{M} \\ \mathrm{F} & \mathrm{F} & \mathrm{M} & \mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{M} \end{array} $$
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