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Asked by aastharoy997 | 29 May, 2020, 01:27: PM
Question: The average of 13 observations is 50. The average of first seven observations is 45 and the average of last seven observations is 52. Find the approximate value of seventh observation.
Solution:
Let the 13 observations be a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12 and a13
Average of first seven observations is 45 which means sum of the first seven observations is 45 x 7 = 315
a1+a2+a3+a4+a5+a6+a7 = 315 ... (i)
Average of last seven observations is 52 which means sum of the last seven observations is 52 x 7 = 364
a7+a8+a9+a10+a11+a12+a13 = 364 ... (ii)
Average of all 13 observations is 50 which means sum of 13 observations is 650
a1+a2+a3+a4+a5+a6+a7+a8+a9+a10+a11+a12+a13 = 650 ... (iii)

Adding (i) and (ii), we get
(a1+a2+a3+a4+a5+a6+a7)+(a7+a8+a9+a10+a11+a12+a13) = 315+364
a1+a2+a3+a4+a5+a6+a7+a8+a9+a10+a11+a12+a13+a= 679
650 + a7 = 679 ... From (iii)
a7 = 29
Hence, the value of seventh observation is 29.
Answered by Renu Varma | 29 May, 2020, 06:35: PM

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