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What happens to the mean when every value in a data set is increased by 5?
- a)The mean stays the same.
- b)The mean increases by 5.
- c)The mean cannot be determined.
- d)The mean decreases by 5.
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
What happens to the mean when every value in a data set is increased b...
When a fixed number, such as 5, is added to each value in the data set, the mean increases by that same number. This is because the overall distribution of the data remains the same, just shifted higher.
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What happens to the mean when every value in a data set is increased b...
Understanding the Mean
The mean, or average, is calculated by adding all the values in a data set and dividing by the number of values.
Effect of Increasing Each Value
When every value in a data set is increased by 5, the overall impact on the mean can be understood as follows:
1. Calculation of the Original Mean
- Original mean = (Sum of original values) / (Number of values)
2. New Values After Increase
- If each value is increased by 5, the new set of values can be represented as:
- New value = Original value + 5
3. Calculation of the New Mean
- New mean = (Sum of new values) / (Number of values)
- New mean = (Sum of original values + (5 * Number of values)) / (Number of values)
- This simplifies to:
- New mean = (Original sum + 5 * Number of values) / (Number of values)
4. Impact on the Mean
- The original sum is essentially just part of the calculation for the new mean.
- Therefore, the new mean is simply the original mean plus 5.
Conclusion
Thus, when every value in a data set is increased by 5, the mean also increases by 5. Hence, the correct answer is option 'B'. This illustrates how the mean is directly affected by constant additions to each data point in the set.
The mean, or average, is calculated by adding all the values in a data set and dividing by the number of values.
Effect of Increasing Each Value
When every value in a data set is increased by 5, the overall impact on the mean can be understood as follows:
1. Calculation of the Original Mean
- Original mean = (Sum of original values) / (Number of values)
2. New Values After Increase
- If each value is increased by 5, the new set of values can be represented as:
- New value = Original value + 5
3. Calculation of the New Mean
- New mean = (Sum of new values) / (Number of values)
- New mean = (Sum of original values + (5 * Number of values)) / (Number of values)
- This simplifies to:
- New mean = (Original sum + 5 * Number of values) / (Number of values)
4. Impact on the Mean
- The original sum is essentially just part of the calculation for the new mean.
- Therefore, the new mean is simply the original mean plus 5.
Conclusion
Thus, when every value in a data set is increased by 5, the mean also increases by 5. Hence, the correct answer is option 'B'. This illustrates how the mean is directly affected by constant additions to each data point in the set.
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