ii) The mean of a set of 20 observations is19.3. The mean is reduced b

1.	ii) The mean of a set of 20 observations is19.3. The mean is reduced by 0.5 whena new observation is added to the set.Find the new mean.
Answer» Given - Mean of 20 observations = 19.3 Mean = Sum of observations/Total number of observations ⇒ 19.3 = Sum of 20 observations/20 ⇒ Sum of 20 observations = 2019.3 Sum of 20 observations = 386 When a new observation is added then the new mean decreases by 0.5 Then, Mean of 21 observations = Sum of 21 observations/21 ⇒ 19.3 - 0.5 = Sum of 20 observations + 21st observation/21 ⇒ 18.8 = 386 + 21st observation/21 ⇒ 386 + 21st observation = 18.821⇒ 386 + 21st observation = 394.8 ⇒ 21st observation = 394.8 - 386 ⇒ 21st observation = 8.8 So, 21st observation is 8.8 New mean = 394.8/21 New Mean = 18.8

ii) The mean of a set of 20 observations is19.3. The mean is reduced by 0.5 whena new observation is added to the set.Find the new mean.

Answer»

Given -

Mean of 20 observations = 19.3

Mean = Sum of observations/Total number of observations

⇒ 19.3 = Sum of 20 observations/20

⇒ Sum of 20 observations = 20*19.3

Sum of 20 observations = 386

When a new observation is added then the new mean decreases by 0.5

Then,

Mean of 21 observations = Sum of 21 observations/21

⇒ 19.3 - 0.5 = Sum of 20 observations + 21st observation/21

⇒ 18.8 = 386 + 21st observation/21

⇒ 386 + 21st observation = 18.8*21⇒ 386 + 21st observation = 394.8

⇒ 21st observation = 394.8 - 386

⇒ 21st observation = 8.8

So, 21st observation is 8.8

New mean = 394.8/21

New Mean = 18.8