Changing the Data Value of 4 to 1

Oct 13, 2025 by miodeya.com 4 views

Original Set Analysis

The original set is given as {2, 4, 6, 2, 6, 1, 5, 1, 6}. To understand the median and mode of this set, we need to first arrange the numbers in ascending order.

Arranging the Original Set in Ascending Order

{1, 1, 2, 2, 4, 5, 6, 6, 6}

Understanding the Median

The median is the middle value of a set when it is arranged in ascending order. Since the original set has 9 numbers, the median will be the 5th number in the set.

Identifying the Median of the Original Set

The 5th number in the set is 4.

Understanding the Mode

The mode is the number that appears most frequently in a set. In the original set, the numbers 1 and 6 appear twice, while the number 2 appears twice as well. However, the number 6 appears three times, making it the mode of the original set.

Identifying the Mode of the Original Set

The mode of the original set is 6.

Changing the Data Value of 4 to 1

Now, let's change the data value of 4 to 1 in the original set.

New Set Analysis

The new set is given as {1, 1, 2, 2, 1, 5, 6, 6, 6}. To understand the median and mode of this new set, we need to first arrange the numbers in ascending order.

Understanding the Median of the New Set

The new set has 9 numbers, so the median will be the 5th number in the set.

Identifying the Median of the New Set

The 5th number in the set is 1.

Understanding the Mode of the New Set

The mode is the number that appears most frequently in a set. In the new set, the numbers 1 and 6 appear twice, while the number 2 appears twice as well. However, the number 1 appears three times, making it the mode of the new set.

Identifying the Mode of the New Set

The mode of the new set is 1.

Comparing the Original and New Sets

Now, let's compare the original and new sets to understand how changing the data value of 4 to 1 affects the median and mode.

Comparing the Medians

The median of the original set is 4, while the median of the new set is 1. This means that changing the data value of 4 to 1 decreases the median.

Comparing the Modes

The mode of the original set is 6, while the mode of the new set is 1. This means that changing the data value of 4 to 1 changes the mode.

Conclusion

Changing the data value of 4 to 1 in the original set affects the median and mode. The median decreases from 4 to 1, and the mode changes from 6 to 1.

Correct Answer

The correct answer is:

D. The median decreases.
C. The mode changes.

Incorrect Answers

The incorrect answers are:

A. The median increases.
B. The median remains the same.
E. The mode remains the same.

Final Thoughts

Changing a data value in a set can significantly affect the median and mode. Understanding how these changes occur is essential in data analysis and statistics.

Frequently Asked Questions

Q1: What happens to the median when a data value is changed from 4 to 1 in the original set?

A1: The median decreases from 4 to 1.

Q2: What happens to the mode when a data value is changed from 4 to 1 in the original set?

A2: The mode changes from 6 to 1.

Q3: Why does the median decrease when a data value is changed from 4 to 1?

A3: The median decreases because the new value (1) is smaller than the original median (4). This changes the middle value of the set, resulting in a decrease in the median.

Q4: Why does the mode change when a data value is changed from 4 to 1?

A4: The mode changes because the new value (1) appears more frequently than the original mode (6). This changes the number that appears most frequently in the set, resulting in a change in the mode.

Q5: What is the impact of changing a data value on the median and mode in general?

A5: Changing a data value can significantly affect the median and mode. The median may increase, decrease, or remain the same, depending on the new value. The mode may also change, depending on the frequency of the new value.

Q6: How can I determine the impact of changing a data value on the median and mode?

A6: To determine the impact of changing a data value on the median and mode, you need to arrange the numbers in ascending order, identify the median and mode, and then compare the results before and after the change.

Q7: What are some common mistakes to avoid when changing a data value?

A7: Some common mistakes to avoid when changing a data value include:

Not arranging the numbers in ascending order
Not identifying the median and mode correctly
Not comparing the results before and after the change
Not considering the impact of the change on the median and mode

Q8: How can I apply this knowledge in real-world scenarios?

A8: You can apply this knowledge in real-world scenarios by:

Analyzing data sets to understand the impact of changing a data value on the median and mode
Identifying patterns and trends in data sets
Making informed decisions based on the analysis of data sets

Q9: What are some additional tips for working with data sets?

A9: Some additional tips for working with data sets include:

Always arranging the numbers in ascending order
Identifying the median and mode correctly
Comparing the results before and after any changes
Considering the impact of the change on the median and mode
Applying this knowledge in real-world scenarios

Q10: How can I further develop my skills in working with data sets?

A10: You can further develop your skills in working with data sets by:

Practicing with different data sets
Analyzing real-world data sets
Reading books and articles on data analysis and statistics
Taking online courses or attending workshops on data analysis and statistics

Conclusion

Changing a data value can significantly affect the median and mode. Understanding how these changes occur is essential in data analysis and statistics. By following the tips and advice provided in this article, you can develop your skills in working with data sets and make informed decisions based on the analysis of data sets.