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Use the data set \(\\{1,3,14,28,2,18\), \(27,86,34,45,44,36,21,11,51,23,37,52,29,41,33\), \(19,24,38,15,87\\}\). What is the mode of the data set? A. 28.5 B. 31.5 C. 86 D. There is no mode.

Short Answer

Expert verified
D. There is no mode.

Step by step solution

01

Define the Mode

The mode of a data set is the number or numbers that appear most frequently. If no number repeats, the data set has no mode.
02

Organize Data

List all the numbers in the data set: \[\{1, 3, 14, 28, 2, 18, 27, 86, 34, 45, 44, 36, 21, 11, 51, 23, 37, 52, 29, 41, 33, 19, 24, 38, 15, 87\}\]
03

Identify Frequency of Each Number

Count how many times each number appears in the data set. 1: 1 time3: 1 time14: 1 time28: 1 time2: 1 time18: 1 time27: 1 time86: 1 time34: 1 time45: 1 time44: 1 time36: 1 time21: 1 time11: 1 time51: 1 time23: 1 time37: 1 time52: 1 time29: 1 time41: 1 time33: 1 time19: 1 time24: 1 time38: 1 time15: 1 time87: 1 time
04

Determine the Mode

Since each number appears only once, there is no number that appears more frequently than others.

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Key Concepts

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

headline of the respective core concept
To understand and identify the mode of a data set, the first step is to organize the data effectively. Organizing data helps you see patterns and outliers more easily.
Begin by listing all the numbers in the data set in a logical order. This could be numerical order, from smallest to largest, or simply noting each entry clearly. In our exercise, we have the dataset: \[ \{1, 3, 14, 28, 2, 18, 27, 86, 34, 45, 44, 36, 21, 11, 51, 23, 37, 52, 29, 41, 33, 19, 24, 38, 15, 87\} \]
By organizing the data set in this manner, we make it easier to move onto the next step, which involves counting the frequency of each number.
headline of the respective core concept
With the data neatly organized, the next step is to count how frequently each number appears in the dataset. Counting frequency tells us how often each number occurs and helps us in identifying modes.
To count the frequency, go through the list of numbers one by one and keep a tally of how many times each number appears. For our dataset, each number appears exactly once:
  • 1: 1 time
  • 3: 1 time
  • 14: 1 time
  • 28: 1 time
  • 2: 1 time
  • 18: 1 time
  • 27: 1 time
  • 86: 1 time
  • 34: 1 time
  • 45: 1 time
  • 44: 1 time
  • 36: 1 time
  • 21: 1 time
  • 11: 1 time
  • 51: 1 time
  • 23: 1 time
  • 37: 1 time
  • 52: 1 time
  • 29: 1 time
  • 41: 1 time
  • 33: 1 time
  • 19: 1 time
  • 24: 1 time
  • 38: 1 time
  • 15: 1 time
  • 87: 1 time
This counting confirms that all numbers in the dataset occur exactly once.
headline of the respective core concept
Identifying the mode becomes straightforward once we have the frequencies of all numbers. The mode is the number that appears most frequently in a dataset. However, if no number repeats more than others, then the data set has no mode.
In our dataset, since each number appears only once, no number is more frequent than another. Therefore, our conclusion is simple: there is no mode in this data set.
This example highlights that not all datasets will have a mode and reinforces the importance of counting frequencies accurately to draw valid conclusions on modes.

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Most popular questions from this chapter

Mrs. Webster surveyed her class of 20 students. She asked each student to identify his or her favorite sport out of a list of five sports. Each student could only choose one sport and everyone participated. The results of the survey are shown in the chart. $$ \begin{array}{|l|l|} \hline \text { Football } & 8 \\ \hline \text { Basketball } & 5 \\ \hline \text { Baseball } & 4 \\ \hline \text { Soccer } & 2 \\ \hline \text { Hockey } & 1 \\ \hline \end{array} $$ If five more students join the class and all five chose soccer as their favorite sport, what percent of the class now favors soccer? A. \(10 \%\) B. \(28 \%\) C. \(32 \%\) D. \(35 \%\)

Use the data set $$ \\{2,11,8,10,6,11,7,14,20,9,1\\} . $$ If an integer \(x\) is added to the data set and \(x \geq 10\), what is the median of the set? A. 9.5 B. 10 C. 18 D. 19

$$ \begin{aligned} &\text { Elena's math scores }\\\ &\begin{array}{|l|l|} \hline \text { Test 1 } & 78 \\ \hline \text { Test 2 } & 83 \\ \hline \text { Test 3 } & 81 \\ \hline \text { Midterm exam } & 85 \\ \hline \text { Test 4 } & 89 \\ \hline \text { Test 5 } & 94 \\ \hline \text { Final Exam } & 96 \\ \hline \end{array} \end{aligned} $$ What is the mode of Elena’s math grades? A. 85 B. 86 C. 87 D. There is no mode

Use the data set \(\\{1,3,14,28,2,18\), \(27,86,34,45,44,36,21,11,51,23,37,52,29,41,33\), \(19,24,38,15,87\\}\). Which, if any, of the data might be considered outliers? Write your answer in the blank.

Terri has grades of 75, 87, 96, 75, and 88 prior to the final exam in her math class. If all the grades are weighted equally, what would Terri need to make on the final exam to average an \(A\) in the class ( \(A\) ranges between 90 and 100 points)? A. 90 B. 95 C. 100 D. It is impossible for her to get an A with those grades.

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