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Chapter 22: Problem 14

Use the following sets of numbers. A: 3,6,4,2,5,4,7,6,3,4,6,4,5,7,3 B: 25,26,23,24,25,28,26,27,23,28,25 C: 0.48,0.53,0.49,0.45,0.55,0.49,0.47,0.55,0.48,0.57, 0.51,0.46,0.53,0.50,0.49,0.53 D: 105,108,103,108,106,104,109,104,110,108,108, 104,113,106,107,106,107,109,105,111,109,108 Determine the mode of the numbers of the given set. Set \(B\)

Short Answer

Expert verified
The mode of set B is 25.

Step by step solution

01

Understanding Mode

The mode of a set of numbers is the number that appears most frequently in the set. To find the mode, we look for the number that occurs more often than any others.
02

List the Numbers in Set B

Given numbers in set B are 25, 26, 23, 24, 25, 28, 26, 27, 23, 28, 25.
03

Count the Frequency of Each Number

Count how many times each number appears in set B: - 23 appears 2 times. - 24 appears 1 time. - 25 appears 3 times. - 26 appears 2 times. - 27 appears 1 time. - 28 appears 2 times.
04

Identify the Mode

The number that appears the most frequently is the mode. In set B, the number 25 appears 3 times, which is more than any other number.

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Key Concepts

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

Understanding Mode
The mode is a statistical term referring to the number that appears most frequently in a data set. In any set of numbers, there can be one mode, more than one mode, or no mode at all.
To determine the mode, you need to count the frequency of each number's occurrence and identify which number or numbers occur the most.
In some data sets, all numbers may occur at the same frequency, which would result in no mode, while others may have more than one number that appears at the highest frequency, resulting in multiple modes.
To summarize:
  • If one number appears more frequently than any others, it is the mode.
  • If two or more numbers appear at the same highest frequency, the data set is multimodal.
  • If no number repeats, the data set has no mode.
Data Analysis Basics
Data analysis involves examining, cleaning, transforming, and modeling data to discover useful information and support decision-making.
When performing data analysis, particularly for determining the mode, consider the following elements:
  • Collection: Gathering relevant data points is the first step. Data must be accurate and representative.
  • Organization: Arranging data in a meaningful order, such as from smallest to largest, can simplify the identification of patterns, including the mode.
  • Counting Occurrences: For identifying the mode, you need to accurately count how often each data point appears.
Effective data analysis not only helps in finding the mode but also reveals other patterns and insights that can inform further statistical evaluations.
The insights gathered from data analysis can be pivotal for making informed decisions in various fields, from business strategies to scientific research.
Frequency Distribution
A frequency distribution is a summary that shows how often each value occurs in a data set.
It's one of the most straightforward forms of organizing data, allowing us to quickly see which values are most frequent, and thus easily identify the mode. Creating a frequency distribution involves several steps:
  • List Unique Values: Write down each unique value in the data set.
  • Tally Counts: For each unique value, count how many times it appears in the data set.
  • Display the Information: Use a chart or a list to display each unique value alongside its frequency.
This method of data representation is incredibly useful not only for finding the mode but also for visualizing data at a glance, understanding variability, and making predictions.
By comprehending the frequency distribution, one can derive deeper insights into the characteristics of the data set.

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Most popular questions from this chapter

Use the following data. The lifetimes of a certain type of automobile tire have been found to be distributed normally with a mean lifetime of \(100,000 \mathrm{km}\) and a standard deviation of \(10,000 \mathrm{km}\) Answer the following questions for a sample of 5000 of these tires. What percent of the samples of 5000 of these tires should have a mean lifetime of more than \(100,282 \mathrm{km} ?\)

Use the following data. A telephone company rechecks the entries for 1000 of its new customers each week for name, address, and phone number. The data collected regarding the number of new accounts with errors, along with the proportion of these accounts with errors, is given in the following table for a \(20-\) wk period: $$\begin{array}{c|c|c} \text {Week} & \text {Accounts with Errors} & \text {Proportion with Errors} \\\ \hline 1 & 52 & 0.052 \\ 2 & 36 & 0.036 \\ 3 & 27 & 0.027 \\ 4 & 58 & 0.058 \\ 5 & 44 & 0.044 \\ 6 & 21 & 0.021 \\ 7 & 48 & 0.048 \\ 8 & 63 & 0.063 \\ 9 & 32 & 0.032 \\ 10 & 38 & 0.038 \\ 11 & 27 & 0.027 \\ 12 & 43 & 0.043 \\ 13 & 22 & 0.022 \\ 14 & 35 & 0.035 \\ 15 & 41 & 0.041 \\ 16 & 20 & 0.020 \\ 17 & 28 & 0.028 \\ 18 & 37 & 0.037 \\ 19 & 24 & 0.024 \\ 20 & 42 & 0.042 \\ \hline \text { Total } & 738 & \end{array}$$ For a \(p\) chart, find the values for the central line, UCL, and LCL.

Find the indicated quantities.In testing a braking system, the distance required to stop a car from \(70 \mathrm{mi} / \mathrm{h}\) was measured in 120 trials. The results are shown in the following distribution table:$$\begin{array}{l|c|c|c|c} \text {Stopping Distance (ft) } & 155-159 & 160-164 & 165-169 & 170-174 \\\\\hline \text {Times Car Stopped} & 2 & 15 & 32 & 36 \end{array}$$.$$\begin{array}{l|c|c|c}\text {Stopping Distance (ft) } & 175-179 & 180-184 & 185-189 \\\\\hline \text {Times Car Stopped} & 24 & 10 & 1\end{array}$$. Form a relative frequency distribution table for these data.

Solve the given problems. With \(5.8 \%\) of the area under the normal curve between \(z_{1}\) and \(z_{2}\) to the left of \(z_{2}=2.0,\) find \(z_{1}\)

Find the indicated quantities.Toss four coins 50 times and tabulate the number of heads that appear for each toss. Draw a frequency polygon showing the number of tosses for which \(0,1,2,3,\) or 4 heads appeared. Describe the distribution (is it about what should be expected?).
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