contestada

A sample consisting of four pieces of luggage was selected from among those checked at an airline counter, yielding the following data on x = weight (in pounds). x1 = 33.2, x2 = 27.6, x3 = 36.9, x4 = 30.7 Suppose that one more piece is selected and denote its weight by x5. Find all possible values of x5 such that x = sample median. (Enter your answers as a comma-separated list.)

Respuesta :

pedrocarratore

Answer:

x5 = 25.1 lb, 32.1 lb, 37.6 lb.

Step-by-step explanation:

The sum of the weight of the four given luggages is:

[tex]S= 33.2+27.6+36.9+30.7 = 128.4\ lb[/tex]

We want to find a value for x5 that yields a sample mean equal to the sample median.

Assuming x1 = 33.2 as the median:

[tex]\frac{128.4+x_5}{5}=33.2 \\x_5=37.6\ lb[/tex]

Assuming x4 = 30.7 as the median:

[tex]\frac{128.4+x_5}{5}=30.7 \\x_5=25.1\ lb[/tex]

Assuming x5 as the median:

[tex]\frac{128.4+x_5}{5}=x_5 \\x_5=32.1\ lb[/tex]

x2 and x3 cannot be the median since they are the lowest and highest value in the set, respectively.

All possible values are x5 = 25.1 lb, 32.1 lb, 37.6 lb.