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Chapter 5: Problem 384

Identify the mode. $$8 , 5 , 1 , 3 , 7 , 1 , 1 , 7 , 1 , 8 , 7$$

Short Answer

Expert verified
The mode is 1.

Step by step solution

01

- Arrange the Data

Organize the data set in ascending order to make it easier to identify the frequencies of each number. So the sorted data is: 1, 1, 1, 1, 3, 5, 7, 7, 7, 8, 8.
02

- Count the Frequencies

Count the number of times each value appears in the data set: 1 appears 4 times, 3 appears 1 time, 5 appears 1 time, 7 appears 3 times, 8 appears 2 times.
03

- Identify the Mode

The mode is the number that appears most frequently in the data set. From the frequency count, 1 appears the most often (4 times). Therefore, 1 is the mode.

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Key Concepts

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

frequency in statistics
Frequency in statistics refers to the number of times a particular value appears in a data set. When you deal with data, it鈥檚 important to identify how often each number occurs to understand the dataset better.
Why is frequency important? Knowing the frequency of values helps you gain insights into the data. For instance:
  • It highlights the most common values, helping identify trends.
  • It is used in various statistical methods and calculations.
  • It assists in decision-making processes based on data analysis.
Counting the frequencies involves organizing and tallying each instance a value appears. This leads us into our next concept: sorting data sets.
sorting data sets
Sorting data sets means arranging the data in a specific order, often ascending or descending. This step is crucial in simplifying the process of analyzing data and identifying patterns. The sorted data set provided in the exercise is:
  • 1, 1, 1, 1, 3, 5, 7, 7, 7, 8, 8

How does sorting help? Sorting data helps in numerous ways:
  • Easier identification of frequencies since all identical values are grouped together.
  • Facilitates quick visual inspection to observe the distribution of the data.
  • Helps in further statistical calculations such as mean, median, and mode.
By first sorting the data, you lay a strong foundation for accurately determining the mode, which brings us to our next section.
identifying mode
The mode is a measure of central tendency and is defined as the value that appears most frequently in a data set. Identifying the mode involves a few straightforward steps:
Step-by-Step to Identify Mode:
  • Sort the data set. This helps in easily spotting the value with the highest frequency.
  • Count the occurrences of each value. In our example, the frequencies are:
    • 1 appears 4 times
    • 3 appears 1 time
    • 5 appears 1 time
    • 7 appears 3 times
    • 8 appears 2 times
  • Find the highest frequency. The value with the highest count is the mode.
In the given exercise, the value 1 appears 4 times, making it the mode of the data set.
Why is Mode Useful? The mode is particularly useful in understanding the most common value or trend in your data. It is often used in:
  • Market research to identify popular products.
  • Education to determine common test scores.
  • Any field where identifying the most frequently occurring value is critical.

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Most popular questions from this chapter

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