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Chapter 22: Problem 13

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 \(A\)

Short Answer

Expert verified
The mode of set A is 4.

Step by step solution

01

Understand the Concept of Mode

The mode of a data set is the value that appears most frequently. In a set of numbers, it is the number that repeats the most.
02

List the Numbers from Set A

Write out all the numbers in set A for easier comparison: 3, 6, 4, 2, 5, 4, 7, 6, 3, 4, 6, 4, 5, 7, 3.
03

Count the Frequency of Each Number

Count how many times each number appears in the set. 3 appears 3 times, 6 appears 3 times, 4 appears 4 times, 2 appears 1 time, 5 appears 2 times, and 7 appears 2 times.
04

Determine the Mode

Identify the number with the highest frequency. The number 4 appears 4 times, which is more frequently than any other number in the set.

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Key Concepts

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

Frequency Distribution
The concept of frequency distribution is crucial in data analysis. It refers to the way in which numbers or observations are spread out across different values or categories. One way to understand this is to imagine organizing a classroom library by genres, with each genre representing a different category.

In statistical terms:
  • The frequency of a number is how many times it appears in the dataset.
  • The frequency distribution is a summary that shows the frequency of each value in a set.
By creating a frequency distribution, you can see how data is distributed. This is done by listing each number in the dataset and counting its occurrences, as was done with the numbers from Set A in the original exercise. Observing these frequencies helps to understand which numbers are common and which are rare.
Data Analysis
Data analysis involves examining, cleaning, transforming, and modeling data to discover useful information. It鈥檚 a bit like being a detective, sifting through data to uncover patterns and stories it might tell. In our exercise, we analyzed Set A to find the mode.

Using data analysis techniques:
  • We began by listing out all numbers in the dataset clearly.
  • Next, we organized the data to better see patterns by counting each number's frequency.
  • Finally, we identified the mode by seeing which number appeared the most.
Through systematic analysis, we were able to determine that the number 4 was the mode. This simple exercise in data analysis can also be applied to more complex datasets to find averages, trends, and insights.
Statistical Concepts
Statistics is the science of collecting, analyzing, presenting, and interpreting data. Fundamental statistical concepts provide tools that help to understand and represent complex data simply. In our case, these concepts were used to find the mode from a dataset in Set A.

Important statistical concepts related to mode include:
  • Central Tendency: It includes the mean, median, and mode, each representing different ways to find the center or typical value in a dataset. Mode specifically represents the most common value.
  • Variability: This describes how spread out values in a dataset are. While we didn't tackle variability directly here, it's key in broader statistical analysis.
  • Frequency: Understanding how often each value appears aids in representing data and identifying patterns, like finding the mode.
Grasping these statistical concepts helps in tasks ranging from simple mode calculation to more advanced data summarization and probability analysis.

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Most popular questions from this chapter

The required data are those in Exercises \(22.1 .\) Find the indicated measure of central tendency. The diameters of a sample of fiber-optic cables were measured (to the nearest \(0.0001 \mathrm{mm}\) ) with the following results.$$\begin{array}{l|c|c|c|c|c} \text {Diameter (mm)} & 0.0057 & 0.0058 & 0.0059 & 0.0060 & 0.0061 \\ \hline \text {No. Cables} & 18 & 36 & 50 & 65 & 31 \end{array}$$ Find the mean of the diameters.

Use the following information. If the weights of cement bags are normally distributed with a mean of 60 lb and a standard deviation of 1 lb, use the empirical rule to find the percent of the bags that weigh the following: Between 59 lb and 61 lb

Find the equation of the least-squares line for the given data. Graph the line and data points on the same graph. In an electrical experiment, the following data were found for the values of current and voltage for a particular element of the circuit. Find the voltage \(V\) as a function of the current \(i .\) Then predict the voltage if \(i=8.00 \mathrm{mA} .\) Is this interpolation or extrapolation? $$\begin{array}{l|l|l|l|l|l} \text {Current }(\mathrm{mA}) & 15.0 & 10.8 & 9.30 & 3.55 & 4.60 \\ \hline \text {Voltage}(\mathrm{V}) & 3.00 & 4.10 & 5.60 & 8.00 & 10.50 \end{array}$$

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 mean of the numbers of the given set. Set \(B\)

Use the following data. It has been previously established that for a certain type of AA battery (when newly produced), the voltages are distributed normally with \(\mu=1.50 \mathrm{V}\) and \(\sigma=0.05 \mathrm{V}\). What percent of the batteries have voltages below \(1.54 \mathrm{V} ?\)
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