Question

higher order thinking the dot plots below show the approximate distances players on two soccer teams had to travel to get to the soccer field for their game. which measure of center should be used to make a comparative inference about the distances traveled by players from each team? use this measure of center to form a comparative inference.

Explanation:

Step1: Analyze Data Distribution

Check if data is symmetric or skewed. Both dot plots have skewed data (Parkview: left-skewed? Wait, no—Parkview has more dots on left (lower distances), Jackson on right? Wait, no, Parkview: dots at 10,15,20,25,30; Jackson: dots at 25,30,35,40,45. Wait, actually, Parkview's data is left-skewed? No, wait, Parkview has more low distances, Jackson more high. So median is better for skewed data (since mean is affected by outliers/skew).

Step2: Calculate Median for Each Team

• Parkview Panthers: Count dots. Let's count: 10:2, 15:6, 20:6, 25:2, 30:1? Wait, no, looking at the dot plot: 10 (2 dots), 15 (let's see: vertical dots at 15: 6? Wait, the first plot: 10 has 2, 15 has, say, 5? Wait, maybe better to find the middle value. Total number of players: let's count Parkview: 2 (10) + 5 (15) + 6 (20) + 2 (25) + 1 (30)? Wait, no, the dot plot for Parkview: 10 (2), 15 (let's see the vertical stack: 15 has 5? Wait, maybe I miscount. Alternatively, median is the middle value. For Jackson Jaguars: dots at 25 (1), 30 (2), 35 (5), 40 (5), 45 (2)? Wait, no, the dot plot: 25 (1), 30 (2), 35 (let's see: vertical stack at 35: 5? 40: 5? 45: 2? Wait, maybe total number of players: let's assume each team has, say, n players. Let's count Parkview: 10 (2) + 15 (5) + 20 (6) + 25 (2) + 30 (1) = 16? Wait, 2+5=7, +6=13, +2=15, +1=16. So median is average of 8th and 9th term. 10:2, 15:5 (total 7), so 8th and 9th are at 15? Wait, no, 10 (2), 15 (let's say 6 dots: 2+6=8, so 8th term at 15, 9th at 20? Wait, maybe I'm overcomplicating. The key is: for skewed data, median is better. So median of Parkview is lower (since more low distances), median of Jackson is higher (more high distances).

Step3: Comparative Inference

Since median is less affected by skew, use median. The median distance for Parkview Panthers is less than the median distance for Jackson Jaguars. So players on Parkview Panthers traveled a shorter median distance than Jackson Jaguars.

Answer:

The measure of center to use is the median (because the data is skewed, median is robust to skew). The median distance traveled by Parkview Panthers players is less than the median distance traveled by Jackson Jaguars players, indicating Parkview players traveled a shorter typical distance to the soccer field.