The line plot shows the heights of the players on a basketball team, in inches.

Question

A line plot named "Heights of Players" shows data from sixty-eight to seventy-four inches. Sixty-eight and one-half has one dot. Sixty-nine and one-half has three dots. Seventy has one dot. Seventy-one has four dots. Seventy-one and one-half has two dots. Seventy-four has one dot.

Part A
Which of the following statements are true? Select all that apply.

(1 point)
Responses

More players are 70
inches tall than are 6912
inches tall.

More players are 70 inches tall than are 69 1 2 inches tall.

More than half of the players are taller than 7012
inches.

More than half of the players are taller than 70 1 2 inches.

There are no players that are 6812
inches tall.

There are no players that are 68 1 2 inches tall.

There are 4
players that are 71
inches tall.

There are 4 players that are 71 inches tall.

The team is made up of players with 6
different heights.

The team is made up of players with 6 different heights.
Question 2
Part B
The next year, a player who is 71
inches tall is replaced by a player who is 73
inches tall. Otherwise the team remains the same. Is 74
an outlier the next year? Explain.

(1 point)
Responses

No, 74
is not an outlier because it is not very different than the other heights in the data set.

No, 74 is not an outlier because it is not very different than the other heights in the data set.

No, 74
is not an outlier because there are two players with this height.

No, 74 is not an outlier because there are two players with this height.

Yes, 74
is an outlier because it is very different than the other heights in the data set.

Yes, 74 is an outlier because it is very different than the other heights in the data set.

Yes, 74
is an outlier because there is still only 1 player with this height.

Yes, 74 is an outlier because there is still only 1 player with this height.

Answer 1

Let's analyze the statements for Part A based on the line plot provided.

Part A - True Statements:

1. More players are 70 inches tall than are 69 1/2 inches tall.

   • False: 70 inches has 1 dot, and 69 1/2 inches has 3 dots.

2. More players are 70 inches tall than are 69 1/2 inches tall.

   • False: Same reasoning as above.

3. More than half of the players are taller than 70 1/2 inches.

   • False: Adding up the players:
     • 68 1/2: 1
     • 69 1/2: 3
     • 70: 1
     • 71: 4
     • 71 1/2: 2
     • 74: 1
     • Total = 12 players.
     • Players taller than 70 1/2: 4 (71) + 2 (71 1/2) + 1 (74) = 7 players. 7 is not more than half of 12.

4. More than half of the players are taller than 70 inches.

   • True: Players taller than 70 inches are 4 (71) + 2 (71 1/2) + 1 (74) = 7, which is more than half of 12.

5. There are no players that are 68 1/2 inches tall.

   • False: There is 1 player at this height.

6. There are no players that are 68 1/2 inches tall.

   • False: Same reasoning as above (1 player at this height exists).

7. There are 4 players that are 71 inches tall.

   • True: As stated, there are indeed 4 players who are 71 inches tall.

8. The team is made up of players with 6 different heights.

   • True: The heights mentioned constitute 6 distinct measurements: 68 1/2, 69 1/2, 70, 71, 71 1/2, and 74.

True Statements Selection:

• More than half of the players are taller than 70 inches. (True)
• There are 4 players that are 71 inches tall. (True)
• The team is made up of players with 6 different heights. (True)

Part B - Outlier Analysis:

To determine if 74 is an outlier after a 71-inch player is replaced with a 73-inch player, we examine the distribution of the heights:

The new heights after the replacement will be:

• 68 1/2: 1
• 69 1/2: 3
• 70: 1
• 71: 4
• 71 1/2: 2
• 73: 1
• 74: 1

To determine if 74 is an outlier, a common method is to calculate the interquartile range (IQR):

1. Find the median (Q2), which divides the data set in half.
2. Calculate Q1 (first quartile) and Q3 (third quartile) to find the IQR.
3. If 74 is more than 1.5 times the IQR above Q3, it is an outlier.

Since this line plot does not give us the full set of calculations, we can make an informed judgment.

Considering the distribution:

• 74 seems to be at the higher end compared to the other players, especially as most players are in the range of 68 1/2 to 73.

From a common understanding of outlier definitions, the best answer is:

• Yes, 74 is an outlier because it is still only 1 player with this height.

Part B - Outlier Selection:

• Yes, 74 is an outlier because there is still only 1 player with this height.