Question

The arithmetic mean of 14 items is 21 if one more item is added to the distribution the am becomes 17. find the value of newly added item

Answer 1

Hope it helps.................

Answer 2

Given,

The arithmetic mean of 14 items = 21

The arithmetic mean after adding one more item = 17

To Find,

Value of the newly added item.

Solution,

Arithmetic mean = $\frac{Sum of all Items}{No of Items}$

Thus 21 = $\frac{Sum of 14 items}{14}$

⇒ Sum of 14 items = $21$ ×$14$ = $294$

Let's say new item added = $x$

⇒ 17 = $\frac{294+x}{15}$

⇒ $294+x=$ $17$×$15 = 255$

⇒ $x$ = $255 - 294 = - 39$

Henceforth the value of the newly added item is $-39$.