If the mean of 25 observations is 27 and each observation is decreased by 7, then the new mean will be ____.

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Detailed Solution

If the mean of 25 observations is 27 and each observation is decreased by 7, then the new mean will be 20.
Given that the mean of 25 observations is 27 and each observation is decreased by 7. Formula used for mean:
Mean

= Sum of observations Total number of observations

Here, we have,
Mean of 25 observations = 27.
Total number of observations = 25.
Substituting values in the formula, we get,

27 = (Sum of the given observations) 25 Sum of the given observations = 27 × 25 Sum of the given observations = 675

To calculate the new mean, we need to understand that when each observation is decreased by 7 then, the new sum is:

= 675 − 25 × 7 = 500

New Mean= 50025 = 20

Thus, the new mean is 20.

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