Chapter 13.4, Problem 50HP

To determine

To find:Median.

Answer to Problem 50HP

Median $=n$

Explanation of Solution

Given information:

Average of seven consecutive odd integers is $n$ .

Let

  $x$ be one odd integer.

So, other odd integers can be

  $x-6,x-4,x-2,x+2,x+4,x+6$

Therefore,

Total set of seven odd integers are

  $x-6,x-4,x-2,x,x+2,x+4,x+6$

Median of above data is $x$ .

Average of given data is

  $A=\frac{x-6+x-4+x-2+x+x+2+x+4+x+6}{7}$

Given Average of seven consecutive odd integers is $n$ .

Therefore,

Using that

We get

  $\begin{array}{l}\Rightarrow n=\frac{x-6+x-4+x-2+x+x+2+x+4+x+6}{7}\\ \Rightarrow 7n=x-6+x-4+x-2+x+x+2+x+4+x+6\\ \Rightarrow 7n=x+x+x+x+x+x+x+6-6+4-4+2-2\\ \Rightarrow 7n=7x\\ \Rightarrow \frac{7n}{7}=\frac{7x}{7}\\ \Rightarrow n=x\end{array}$

Therefore,

We got $n=x$

Using that

We can say that

Median $=n$