The mean of 1st 8 observations is 18 and last 8 observations is 20.If the mean of all 15 observations is 19.Find th 8th observations
Answers
Answer:
Step-by-step explanation:
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
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Sum of 1st 8 observation = 8 × 18
= 144
Sum of last 8 observation = 8 × 20
= 160
Sum of the 15 observation = 15 × 19
= 285
8th observation =( 144 + 160 ) - 285
= 304 - 285
= 19