Question

1 multiple choice 2 points a certain restaurant hosted a series of birthday parties throughout the month. if the number of attendees at each party is listed below, find the median number of attendees for the month. 125 74 89 56 105 113 55 127 105 97 93 89 91

Explanation:

Step1: Order the data

First, we need to arrange the number of attendees in ascending order. The given data is: 125, 74, 89, 56, 105, 113, 55, 127. After sorting, we get: 55, 56, 74, 89, 105, 113, 125, 127.

Step2: Find the median position

Since there are \( n = 8 \) data points (an even number), the median will be the average of the \( \frac{n}{2} \)-th and \( (\frac{n}{2}+ 1) \)-th values. Here, \( \frac{n}{2}=\frac{8}{2} = 4 \) and \( \frac{n}{2}+1=4 + 1=5 \).

Step3: Identify the relevant values

The 4th value in the sorted list is 89, and the 5th value is 105.

Step4: Calculate the median

To find the median, we take the average of these two values: \( \frac{89 + 105}{2}=\frac{194}{2}=97 \).

Answer:

97