Question

You receive a fax with six bids (in millions of dollars):2.2,1.3,1.9,1.2 2.4 and x is some number that is too blurry to read. Without knowing what x is, the median a. Is 1.9 b. Must be between 1.3 and 2.2 c. Could be any number between 1.2 and 2.4

Answer 1

Answer:

b. Must be between 1.3 and 2.2

Step-by-step explanation:

The formula for calculating median is :

1. When n(number of observations in data) is odd = $(\frac{n+1}{2} )^{th} observation$
2. When n is even = $\frac{(\frac{n}{2})^{th}obs. + (\frac{n}{2} + 1)^{th} obs. }{2}$

Since in our data n is even so we use the formula for calculating median

                  =  $\frac{(\frac{n}{2})^{th}obs. + (\frac{n}{2} + 1)^{th} obs. }{2}$

First arranging data in ascending order we get :

     1.2, 1.3, 1.9, 2.2, 2.4 and since we know nothing about our sixth value x so we assume that it may take any position in our data.

Now there may be cases for which position is x on ;

• If x is the first obs in our data then our median = $\frac{3^{rd}obs + 4^{th}obs }{2}$ = $\frac{1.3+1.9}{2}$  

                                                                                                            = 1.6

• If x is between 1.2 and 1.3 then also median will be 1.6 .

• If x is between 1.3 and 1.9 then median will be somewhere between 1.3 and 1.9 .
• If x is between 1.9 and 2.2 then median will be somewhere between 1.9 and 2.2 .

• And If x is between 2.2 and 2.4 or after 2.4 then median =  $\frac{3^{rd}obs + 4^{th}obs }{2}$

                                                                                         = $\frac{1.9+2.2}{2}$ = 2.05 .

So from all these observations we conclude that without knowing what x median of data must be between 1.3 and 2.2 .