Question

the mean of first 8 observation is 18 & last 8observation is 20 . if thevmean of all 15 observation is 19 find the 8th observation

Answer 1

Given mean of first 8 obs = 18
Then sum of first 8 obs = 18×8 = 144
Mean of last 8 obs = 20
Then sum of last 8 obs = 20×8 = 160
Let the 8th observation be x
Then 144 and 160 both have x
Sum of all 15 observations = 144+160 - x  [as there are 2 x s one in 144 and                                                                          the other in 160 only one x is                                                                              present in total observations]
Mean of all 15 observations is given as 19
⇒ (144 +160 -x)/15 = 19
⇒  304 - x = 19×15
⇒  304 - x = 285
⇒  -x = 285 -304
⇒  -x = -19
∴ x = 19
∴ The 8th observation is 19