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Question
The mean of 11 observations is 12. The mean of first 6 observations is 14 and the mean of last 6 observations is 11. Find the 6th observation.
Sum
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Solution
Given:
Mean of 11 observations = 12
⇒ Total sum of 11 observations
= 11 × 12
= 132
Mean of first 6 observations = 14
⇒ Sum of first 6
= 6 × 14
= 84
Mean of last 6 observations = 11
⇒ Sum of last 6
= 6 × 11
= 66
Step-wise calculation:
1. Sum of first 6 + Sum of last 6
= 84 + 66
= 150
2. But (sum of first 6) + (sum of last 6) = (sum of all 11) + (6th observation) because the 6th observation is counted twice.
3. So, 132 + x6 = 150.
4. Therefore, x6
= 150 – 132
= 18
The 6th observation is 18.
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