#### Question

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

#### Solution

We have,

The mean of 35 observations is 20.

Let *x* be the sum of 35 observations

⇒ mean = `("sum of observations")/("number of observations")`

⇒ 20 = `x/35`

⇒ x = 700

Let *y* be the sum of first 18 observations.

Mean of first 18 observations is 15.

` y / 18 ` = 15

⇒ y = 270

And *z* be the sum of last 18 observations

Mean of last 18 observations is 25.

`z / 18` = 25

⇒ z = 450

let the 18th term be *a*.

18th term is common in first 18 and last 18 observations

x + a = y + z

700 + a = 270 + 450

a = 720 - 700

a = 20

Hence, the 18th observation is 20.

Is there an error in this question or solution?

Solution The Mean of 35 Observations is 20, Out of Which Mean of First 18 Observations is 15 and Mean of Last 18 Observation is 25. Find the 18th Observation. Concept: Measures of Central Tendency.