Question

Use the data to find the upper quartile value.


Movie Ticket Fees at a Local Theater

$10.25 $9.75

$8.75 $12.75

$11.00 $6.50


A $10

B $8.75

C $11

D $12.75

Answer 1

The upper quartile value is $11.

Step-by-step explanation:

We are given the following data to find the upper Quartile value;

Movie Ticket Fees at a Local Theater  :  $6.50, $8.75,  $9.75, $10.25,  $11.00, $12.75.

Upper Quartile value means that there is 75% data values below this upper quartile value.

Now, the upper Quartile is represented as  $Q_3$ and the formula for calculating this value is given by;

                              $Q_3 = 3(\frac{n+1}{4})^{th} \text{ obs.}$

where, n = number of observations in our data = 6 values

So,           $Q_3 = 3(\frac{6+1}{4})^{th} \text{ obs.}$

                $Q_3 = 3(\frac{7}{4})^{th} \text{ obs.}$

                $Q_3 = (\frac{21}{4})^{th} \text{ obs.}$

                $Q_3 = (5.25)^{th} \text{ obs.}$

                $Q_3 = 5^{th} \text{ obs.} + 0.25 ( 6^{th} \text{ obs.}-5^{th} \text{ obs.})$

                $Q_3 =$ $11.00 + 0.25($12.75 - $11.00)

                      =  $11.00 + 0.44

                 $Q_3$ = $11.44 ≈ $11

Therefore, the upper quartile value is $11.