The mean of 35 observations is 20, out of which mean of first 18 obser

1.	The mean of 35 observations is 20, out of which mean of first 18 observations is 15 and mean of last 18 observations is 25. Find the 18th observation.
Answer» \(Mean = \cfrac{The\,sum \,of\, all \,observatiojns }{Total \,number \,of \,observations}\) ∴ The sum of all observations = Mean x Total number of observations The mean of 35 observations is 20 ∴ Sum of 35 observations = 20 x 35 = 700 ...(i) The mean of first 18 observations is 15 Sum of first 18 observations =15 x 18 = 270 …(ii) The mean of last 18 observations is 25 Sum of last 18 observations = 25 x 18 = 450 …(iii) ∴ 18^th observation = (Sum of first 18 observations + Sum of last 18 observations) – (Sum of 35 observations) = (270 + 450) – (700) … [From (i), (ii) and (iii)] = 720 – 700 = 20 The 18^th observation is 20.

The mean of 35 observations is 20, out of which mean of first 18 observations is 15 and mean of last 18 observations is 25. Find the 18th observation.

Answer»

\(Mean = \cfrac{The\,sum \,of\, all \,observatiojns }{Total \,number \,of \,observations}\)

∴ The sum of all observations

= Mean x Total number of observations

The mean of 35 observations is 20

∴ Sum of 35 observations = 20 x 35 = 700 ...(i)

The mean of first 18 observations is 15

Sum of first 18 observations =15 x 18 = 270 …(ii)

The mean of last 18 observations is 25 Sum of last 18 observations = 25 x 18

= 450 …(iii)

∴ 18^th observation = (Sum of first 18 observations + Sum of last 18 observations) – (Sum of 35 observations)

= (270 + 450) – (700) … [From (i), (ii) and (iii)]

= 720 – 700 = 20

The 18^th observation is 20.

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