Question
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  1. What is the mode of the data set?
  2. What is the mean value of the data set?
  3. What is the median value of the data set?

Ask by Vaughan Bright. in South Africa
Jan 21,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

  • Mode: 7
  • Mean: 8.7
  • Median: 8.5

Solution

Let’s analyze the given data set and compute the requested statistical measures step by step.
Data Set:

1. Mode of the Data Set

Definition:
The mode is the value that appears most frequently in a data set.
Steps to Find the Mode:
  • Count the frequency of each number:
    • 7: appears 3 times
    • 8: appears 2 times
    • 9: appears 2 times
    • 10: appears 1 time
    • 11: appears 2 times
Result:
The number 7 appears most frequently (3 times).
Mode = 7

2. Mean Value of the Data Set

Definition:
The mean is the average of all the numbers in the data set.
Steps to Calculate the Mean:
  1. Sum all the numbers:
  2. Count the total number of data points:
    There are 10 numbers.
  3. Divide the total sum by the number of data points:
Mean = 8.7

3. Median Value of the Data Set

Definition:
The median is the middle value when the data set is ordered from smallest to largest. If there’s an even number of observations, it’s the average of the two middle numbers.
Steps to Find the Median:
  1. Order the data set in ascending order:
  2. Determine the middle positions:
    • Since there are 10 data points (even number), the median is the average of the 5th and 6th numbers.
  3. Identify the 5th and 6th numbers:
    • 5th number = 8
    • 6th number = 9
  4. Calculate the median:
Median = 8.5

Summary of Results:
  1. Mode: 7
  2. Mean: 8.7
  3. Median: 8.5

Answered by UpStudy AI and reviewed by a Professional Tutor

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Extra Insights

The mode of the data set is the number that appears most frequently. In this case, both 7 and 9 occur three times, making the modes 7 and 9.
To find the mean value, add all the numbers together and divide by the total count. The sum is . There are 10 numbers, so the mean is .
For the median, first arrange the numbers in ascending order: . With an even number of observations, the median is the average of the two middle numbers (the 5th and 6th terms), which are 8 and 9, giving a median of .

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