Question: The arithmetic mean of three observations is x. If the values of two observations are y and z, what is the value of the third observation?
- x
- y + z – x
- (x + y + z)/3
- (x – y – z)/3
The Arithmetic mean of Three Observations is x Answer:
Solution: In an arithmetic mean problem, the arithmetic mean (often denoted by x̄) is the sum of all the observations divided by the number of observations.
- In this case, we have three observations, so the arithmetic mean can be expressed as: x̄ = (y + z + ?) / 3
- To find the value of the third observation, we can rearrange the equation: y + z +? = x̄ * 3
- Now, to determine the value of the third observation, we subtract the sum of the given observations (y + z) from the product of the arithmetic mean and the number of observations (x̄ * 3):? = (x̄ * 3) – (y + z)
In conclusion, to find the missing observation in an arithmetic mean problem, you can calculate it by subtracting the sum of the known observations from the product of the arithmetic mean and the number of observations.
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