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Chapter 5: Problem 383

Identify the mode. $$2 , 5 , 1 , 5 , 2 , 1 , 2 , 3 , 2 , 3 , 1$$

Short Answer

Expert verified
The mode is 2.

Step by step solution

01

List the Data

Write down the given data set: 2, 5, 1, 5, 2, 1, 2, 3, 2, 3, 1.
02

Tally the Frequency

Count the number of times each number appears in the data set. 1 appears 3 times 2 appears 4 times 3 appears 2 times 5 appears 2 times.
03

Identify the Mode

The mode is the number that appears the most frequently. From the tally, 2 appears 4 times, 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.

frequency tally
Understanding how frequently each number appears in a data set is crucial to many types of data analysis. This process is called a frequency tally. It involves counting the number of times each unique number shows up in a list, which helps us identify patterns and draw conclusions.

To perform a frequency tally:
  • Write down the data set you have.
  • List each unique number.
  • Count how many times each number appears in the data set.
This counting process helps you organize and summarize the data, making it easier to spot trends and make decisions. For instance, in our exercise, we found that the number 2 appears 4 times, while other numbers appear fewer times.
data set analysis
Data set analysis involves examining a collection of numbers to understand what they tell us about the overall group. Analyzing data sets helps us make sense of complex information and draw meaningful conclusions.

Key steps in data set analysis:
  • Start by listing your data set clearly.
  • Use techniques like frequency tally to organize your data.
  • Look for trends, such as which number appears most often (the mode), the range (difference between highest and lowest values), and other statistical measures.
By analyzing the data set provided in the exercise, we can see that different numbers appear with varying frequencies, leading us to the next crucial concept: identifying the most frequent number or the mode.
most frequent number
The most frequent number in a data set is called the mode. It's the number that appears more times than any other. Understanding the mode helps us identify the most common or popular item within a dataset, which can be very useful in various real-world scenarios from customer preference surveys to scientific research.

To identify the mode:
  • First, perform a frequency tally to see how many times each number appears.
  • Compare these counts to find out which number has the highest count.
  • The number with the highest frequency is the mode.
For example, in our exercise, after tallying the frequency of each number, we found that the number 2 has the highest frequency, appearing 4 times. Therefore, 2 is the mode of this data set.

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