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For 36 stones with assumed mean $A=225$, $\sum fd=-750$ and $\sum fd^2=197500$, the mean by the deviation method to three decimal places is:
A204.167
B225.000
C245.833
D204.170
Answer & Solution
Correct answer: A. 204.167
1. The deviation-method mean is $\bar{x}=A+\dfrac{\sum fd}{N}$.
2. Substitute $A=225$, $\sum fd=-750$ and $N=36$.
3. $\dfrac{-750}{36}=-20.8333\ldots$
4. So $\bar{x}=225-20.833=204.167$ to three decimal places.
5. $225$ ignores the correction term; $245.833$ adds instead of subtracting; $204.170$ rounds to three decimals too early.
_Source: NECTA ACSEE 2023 Advanced Mathematics 142/1, Question 4: Statistics_
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