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If each observation of the data is increased by 2, then their mean is
- a)Increased by 2n times
- b)Increased by 2 times
- c)Decreased by 2 times
- d)Remains the same
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
If each observation of the data is increased by 2, then their mean is...
Assume a set of observations are x1,x2,x3,…,xn
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Here the total number of observations is n,
Now, each observation of the data is increased by 2,
So, new observations are 2x1,2x2,2x3,…,2xn
So, the new mean increased by 2 times.
Hence, the correct option is (B).
Most Upvoted Answer
If each observation of the data is increased by 2, then their mean is...
Explanation:
To understand why the mean is increased by 2 times when each observation is increased by 2, we need to understand the concept of the mean and how it is calculated.
The mean, also known as the average, is calculated by summing up all the observations in the data set and then dividing by the total number of observations. Mathematically, it can be represented as:
Mean = (Sum of all observations) / (Total number of observations)
Let's say we have a data set with n observations. If each observation is increased by 2, then the new data set will have the same number of observations, but each observation will be 2 units greater than the original data set.
Example:
Original data set: 1, 3, 5, 7, 9
Increased data set: 3, 5, 7, 9, 11
Now, let's calculate the mean for both the original and increased data sets.
Original data set:
Mean = (1 + 3 + 5 + 7 + 9) / 5 = 5
Increased data set:
Mean = (3 + 5 + 7 + 9 + 11) / 5 = 7
As we can see from the example, the mean of the increased data set is 2 greater than the mean of the original data set. This holds true for any data set where each observation is increased by the same value.
Conclusion:
When each observation of the data is increased by 2, the mean of the data set is increased by 2 times. This is because the increase in each observation contributes equally to the increase in the sum of all observations, resulting in an increase in the mean.
To understand why the mean is increased by 2 times when each observation is increased by 2, we need to understand the concept of the mean and how it is calculated.
The mean, also known as the average, is calculated by summing up all the observations in the data set and then dividing by the total number of observations. Mathematically, it can be represented as:
Mean = (Sum of all observations) / (Total number of observations)
Let's say we have a data set with n observations. If each observation is increased by 2, then the new data set will have the same number of observations, but each observation will be 2 units greater than the original data set.
Example:
Original data set: 1, 3, 5, 7, 9
Increased data set: 3, 5, 7, 9, 11
Now, let's calculate the mean for both the original and increased data sets.
Original data set:
Mean = (1 + 3 + 5 + 7 + 9) / 5 = 5
Increased data set:
Mean = (3 + 5 + 7 + 9 + 11) / 5 = 7
As we can see from the example, the mean of the increased data set is 2 greater than the mean of the original data set. This holds true for any data set where each observation is increased by the same value.
Conclusion:
When each observation of the data is increased by 2, the mean of the data set is increased by 2 times. This is because the increase in each observation contributes equally to the increase in the sum of all observations, resulting in an increase in the mean.
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Community Answer
If each observation of the data is increased by 2, then their mean is...
Assume a set of observations are x1,x2,x3,…,xn
Here the total number of observations is n,
Now, each observation of the data is increased by 2,
So, new observations are 2x1,2x2,2x3,…,2xn
So, the new mean increased by 2 times.
Hence, the correct option is (B).
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If each observation of the data is increased by 2, then their mean isa)Increased by 2n timesb)Increased by 2 timesc)Decreased by 2 timesd)Remains the sameCorrect answer is option 'B'. Can you explain this answer?
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