Question

1. the four box plots below represent playing time for 4 carmen soccer players over their last 16 games.

answer the following questions about the box plots:
a. which player typically plays more minutes per game? which player plays the least? which measure do you use to determine this?
most: ______ least: ______ measure (circle one): center (median) variability (iqr)
b. which player gets more consistent playing time (varies the least)? which player gets the least consistent (varies the most)? which measure do you use to determine this?
most: ______ least: ______ measure (circle one): center (median) variability (iqr)
c. how many games are represented in each interval?
from the minimum to q1? ________
from q1 to the median? ________
from the median to q3? ________
from q3 to the maximum? ________
d. label the minimum, q1, median, q3 and maximum in each box plot graph.

Explanation:

Step1: Identify measure for typical playing - time

To determine which player typically plays more or less minutes per game, we use the median (center of the box - plot) as it represents the middle value of the data set.

Step2: Compare medians for part a

By observing the box - plots, the median of player D is the highest among the four players, and the median of player A is the lowest. So, the player who typically plays more minutes per game is D and the one who plays the least is A.

Step3: Identify measure for consistency

To determine which player has more or less consistent playing time, we use the inter - quartile range (IQR). The IQR is the difference between Q3 and Q1 (Q3 - Q1) and represents the spread of the middle 50% of the data. A smaller IQR indicates more consistent data.

Step4: Compare IQRs for part b

By observing the box - plots, players A, B, and D have relatively larger IQRs compared to player C. So, the players with the most variable playing time are A, B, and D, and the player with the least variable (most consistent) playing time is C.

Step5: Calculate number of games in intervals for part c

Since there are 16 games in total for each player, and the box - plot divides the data into four equal - sized intervals (quartiles), each interval represents $\frac{16}{4}=4$ games. So, from the minimum to Q1: 4 games, from Q1 to the median: 4 games, from the median to Q3: 4 games, from Q3 to the maximum: 4 games.

Step6: Label box - plot for part d

For each box - plot: The left - most point is the minimum, the left edge of the box is Q1, the line inside the box is the median, the right edge of the box is Q3, and the right - most point is the maximum.

Answer:

a. Most: D; Least: A; Measure: Center (median)
b. Most: A, B, D; Least: C; Measure: Variability (IQR)
c. From the minimum to Q1: 4; From Q1 to the median: 4; From the median to Q3: 4; From Q3 to the maximum: 4
d. For each box - plot, label as follows: Minimum (left - most point), Q1 (left edge of the box), Median (line inside the box), Q3 (right edge of the box), Maximum (right - most point)