Class 7 Exam > Class 7 Questions > If each entry of a data is increased by 5, ho...
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If each entry of a data is increased by 5, how does the mean change?
- a)Remains the same .
- b)Increases by 5.
- c)Decreases by 5.
- d)Becomes half.
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If each entry of a data is increased by 5, how does the mean change?a)...
Let the observations be x1,x2,.....xn.A.M.After th
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Most Upvoted Answer
If each entry of a data is increased by 5, how does the mean change?a)...
Explanation:
Increasing each entry of a data set by the same value will have a direct impact on the mean of the data set. Let's break it down further:
- Original Mean: The mean of a data set is calculated by adding up all the values and dividing by the total number of values.
- Effect of Increasing by 5: When each entry of the data set is increased by 5, this means that every value contributing to the mean is now 5 units higher than before. As a result, the sum of all values will increase by 5 times the total number of values in the data set.
- Change in Mean: Since the mean is calculated by dividing the total sum by the number of values, increasing each value by 5 will cause the total sum to increase by 5 times the number of values. Therefore, the mean will also increase by the same value that was added to each entry, which is 5.
Therefore, the correct answer is option 'b) Increases by 5.
Increasing each entry of a data set by the same value will have a direct impact on the mean of the data set. Let's break it down further:
- Original Mean: The mean of a data set is calculated by adding up all the values and dividing by the total number of values.
- Effect of Increasing by 5: When each entry of the data set is increased by 5, this means that every value contributing to the mean is now 5 units higher than before. As a result, the sum of all values will increase by 5 times the total number of values in the data set.
- Change in Mean: Since the mean is calculated by dividing the total sum by the number of values, increasing each value by 5 will cause the total sum to increase by 5 times the number of values. Therefore, the mean will also increase by the same value that was added to each entry, which is 5.
Therefore, the correct answer is option 'b) Increases by 5.
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If each entry of a data is increased by 5, how does the mean change?a)Remains the same .b)Increases by 5. c)Decreases by 5.d)Becomes half.Correct answer is option 'B'. Can you explain this answer?
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