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प्रश्न
The mean of 9 observations is 15. The mean of first 5 observations is 16 and the mean of last 5 observations is 14. Find the 5th observation.
बेरीज
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उत्तर
Given:
Mean of 9 observations = 15
Mean of first 5 = 16
Mean of last 5 = 14
Step-wise calculation:
1. Total sum of 9 observations
= 9 × 15
= 135
2. Sum of first 5 observations
= 5 × 16
= 80
3. Sum of last 5 observations
= 5 × 14
= 70
4. The 5th observation is counted in both the first 5 and last 5.
So, sum (first 5) + sum (last 5) = total sum + 5th observation
⇒ 80 + 70 = 135 + x5
⇒ 150 = 135 + x5
⇒ x5 = 150 – 135
= 15
The 5th observation is 15.
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