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The average of 6 observations is 45.5. If one new observation is added to the previous observation, then the new average becomes 47. The new observation is :
- a)58
- b)56
- c)50
- d)46
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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The average of 6 observations is 45.5. If one new observation is added...
Given:
- Average of 6 observations = 45.5
- Addition of a new observation increases the average to 47
To find:
The value of the new observation
Solution:
Let's assume the sum of the 6 observations is S and the value of the new observation is x.
Step 1: Find the sum of the 6 observations
Given that the average of the 6 observations is 45.5, we can write the equation:
S/6 = 45.5
Multiplying both sides by 6, we get:
S = 273
Step 2: Find the sum of the 7 observations
Including the new observation, the total number of observations becomes 7. The sum of the 7 observations can be written as:
(S + x)
Step 3: Find the new average
Given that the new average is 47, we can write the equation:
(S + x)/7 = 47
Multiplying both sides by 7, we get:
S + x = 329
Step 4: Substitute the value of S from Step 1 into the equation from Step 3
Substituting the value of S as 273 into the equation (S + x = 329), we get:
273 + x = 329
Simplifying the equation, we find:
x = 329 - 273
x = 56
Conclusion:
Thus, the value of the new observation is 56. Therefore, the correct answer is option 'B' (56).
- Average of 6 observations = 45.5
- Addition of a new observation increases the average to 47
To find:
The value of the new observation
Solution:
Let's assume the sum of the 6 observations is S and the value of the new observation is x.
Step 1: Find the sum of the 6 observations
Given that the average of the 6 observations is 45.5, we can write the equation:
S/6 = 45.5
Multiplying both sides by 6, we get:
S = 273
Step 2: Find the sum of the 7 observations
Including the new observation, the total number of observations becomes 7. The sum of the 7 observations can be written as:
(S + x)
Step 3: Find the new average
Given that the new average is 47, we can write the equation:
(S + x)/7 = 47
Multiplying both sides by 7, we get:
S + x = 329
Step 4: Substitute the value of S from Step 1 into the equation from Step 3
Substituting the value of S as 273 into the equation (S + x = 329), we get:
273 + x = 329
Simplifying the equation, we find:
x = 329 - 273
x = 56
Conclusion:
Thus, the value of the new observation is 56. Therefore, the correct answer is option 'B' (56).
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The average of 6 observations is 45.5. If one new observation is added to the previous observation, then the new average becomes 47. The new observation is :a)58b)56c)50d)46e)None of theseCorrect answer is option 'B'. Can you explain this answer?
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