Question

3 four amateur miniature golfers attempt to finish 100 holes under par several times. after each round of 100 holes, the number of holes they successfully complete under par is recorded. due to the presence of extreme values, box plots were determined to be the best representation for the data. list the four box plots in order of variability from least to greatest.
player a
box plot with number line 40, 43, 46, 49, 52, 55, 58, 61, 64, 67, 70
number of holes completed under par
player b
box plot with number line 40, 43, 46, 49, 52, 55, 58, 61, 64, 67, 70
number of holes completed under par
player c
box plot with number line 40, 43, 46, 49, 52, 55, 58, 61, 64, 67, 70
number of holes completed under par
player d
box plot with number line 40, 43, 46, 49, 52, 55, 58, 61, 64, 67, 70
number of holes completed under par
4 from unit 1, lesson 10
select all the distribution shapes for which the median could be much less than the mean.
a symmetric
b bell - shaped
c skewed left
d skewed right
e bimodal

Explanation:

Question 3

Step1: Recall Variability in Box Plots

Variability in box plots is measured by the interquartile range (IQR) and the range (whiskers). A smaller spread (shorter box and whiskers) means less variability.

Step2: Analyze Each Player's Box Plot

• Player D: The box and whiskers are the shortest (narrowest spread).
• Player C: Slightly wider than D but narrower than A and B.
• Player A: Wider than C, narrower than B.
• Player B: The widest spread (longest box and whiskers).

Step3: Order by Variability (Least to Greatest)

Least variability first (smallest spread) to greatest (largest spread). So order: Player D, Player C, Player A, Player B.

• Symmetric (A): Mean ≈ median, so median not much less.
• Bell - shaped (B): Also symmetric, mean ≈ median.
• Skewed left (C): Mean is pulled left (less than median), so median > mean.
• Skewed right (D): Mean is pulled right (greater than median), so median < mean (could be much less).
• Bimodal (E): If skewed right (even with two modes), mean can be much greater than median.

Answer:

Player D, Player C, Player A, Player B

Question 4