Question

The mean of a data set with 10 observations is calculated as 17.85. If one more value is included in the data,then for the new data with 11 observations,mean becomes 18.50. Find the value of this 11th observation

Answer 1

Let 'x' be the sum of 10 observations
Let 'n' be the new observation (or) 11th observation
Sum of observations/No.of observations=Mean
=> x/10 = 17.85
=> x = 17.85 * 10
x = 178.5 ---------- (1)
Sum of 10 observations is 178.5
Sum of observations/No. of observations=Mean
=> (x+n)/11 = 18.50
=> x+n = 18.50 * 11
=> x+n = 203.5 ------------- (2)
Substitute (1) in this equation (2)
=> 178.5+n = 203.5
=> n = 203.5 - 178.5
=> n = 25
Therefore the value of 11th observation is 25

Answer 2

Solution :-

Mean of a data set with 10 observation = 17.85

Mean = Sum of observation/Number of observations

Let the sum of observations be x

⇒ 17.85 = x/10

⇒ x = 17.85*10

⇒ x = 178.5

Sum of 10 observations is 178.5

Now, one more value is added to the data, then the mean of 11 observations is 18.5

⇒ 18.5 = x/11

⇒ x = 18.5*11

⇒ x = 203.5

Sum of 11 observations is 203.5

Now, the difference between the sum of 11 observations and the sum of 10 observations is the value of 11th observation.

⇒ 203.5 - 178.5 = 25

So, the value of 11th observation is 25

Answer.