Question

test practice

1. open response the number of points

seth has earned playing his favorite
game is shown. find the median of
the data.
40, 28, 24, 37, 43, 26, 30, 36

Explanation:

Step1: Order the data

First, we need to arrange the data in ascending order. The given data is 40, 28, 24, 37, 43, 26, 30, 36. Arranging them from smallest to largest: 24, 26, 28, 30, 36, 37, 40, 43.

Step2: Find the median position

The formula to find the position of the median for a set with \( n \) numbers is \( \frac{n + 1}{2} \) when \( n \) is odd, and the average of the \( \frac{n}{2} \)-th and \( (\frac{n}{2}+ 1) \)-th terms when \( n \) is even. Here, \( n = 8 \) (even). So we need the average of the \( \frac{8}{2}=4 \)-th and \( (\frac{8}{2}+ 1)=5 \)-th terms.

Step3: Identify the 4th and 5th terms

From the ordered data: 24 (1st), 26 (2nd), 28 (3rd), 30 (4th), 36 (5th), 37 (6th), 40 (7th), 43 (8th). The 4th term is 30 and the 5th term is 36.

Step4: Calculate the median

The median is the average of these two terms: \( \frac{30 + 36}{2}=\frac{66}{2}=33 \).

Answer:

The median of the data is 33.