Questions: Here are the last 11 audience totals for a small movie theater: 11,12,13,28,32,33,44,47,55,56,82 What is the third quartile of the list above?

Transcript text: /StudentFunctions/Interface/acellus_engine.htm|?Class|D=348051058 Here are the last 11 audience totals for a small movie theater: \[ 11,12,13,28,32,33,44,47,55,56,82 \] What is the third quartile of the list above? [?] $\square$ Enter

Solution

Solution Steps

Step 1: Data Preparation

The given audience totals for the small movie theater are: \[ \text{Data} = [11, 12, 13, 28, 32, 33, 44, 47, 55, 56, 82] \] First, we sort the data, which results in: \[ \text{Sorted Data} = [11, 12, 13, 28, 32, 33, 44, 47, 55, 56, 82] \]

Step 2: Calculate the Rank for the Third Quartile

To find the third quartile ($Q_3$), we use the formula for the rank: \[ \text{Rank} = Q \times (N + 1) \] where $Q = 0.75$ (for the third quartile) and $N = 11$ (the number of data points). Thus, we calculate: \[ \text{Rank} = 0.75 \times (11 + 1) = 0.75 \times 12 = 9.0 \]

Step 3: Determine the Value at the Rank Position

The rank of $9.0$ indicates that the third quartile corresponds to the value at position $9$ in the sorted data. Looking at the sorted list: \[ \text{Value at Position 9} = 55 \]