Question

Team 1
18
22
24
22
18
25
30
33
35
28
22
24
20
Team 2
19
20
26
28
25
29
34
37
39
32
27
26
25


Two teams are playing in the finals for an adult softball league. Each team has 13 players and the ages of the team members are shown in the tables. Which statement is true?
Responses
A The mean for team 1 is greater than the mean for team 2.The mean for team 1 is greater than the mean for team 2.
B The mean for team 2 is greater than the mean for team 1.The mean for team 2 is greater than the mean for team 1.
C The median for team 1 is greater than the median for team 2.The median for team 1 is greater than the median for team 2.
D The value of Q1 for team 1 is greater than the value of Q1 for team 2.

Answer 1

To determine which statement is true, we'll need to calculate the mean and median for both teams, as well as the first quartiles (Q1).

### Team 1 Ages:
18, 22, 24, 22, 18, 25, 30, 33, 35, 28, 22, 24, 20

#### Calculating the mean for Team 1:
Mean = (Sum of ages) / (Number of players)
Sum = 18 + 22 + 24 + 22 + 18 + 25 + 30 + 33 + 35 + 28 + 22 + 24 + 20 = 25 + 30 + 33 + 35 + 28 + 22 + 24 + 20
Sum = 22 + 25 + 30 + 24 + 33 + 35 + 28 + 20
= 22 + 25 + 30 + 24 + 33 + 35 + 28 + 20 = 24 + 22 + 25 + 20 + 22 + 24 + 35 + 30 + 28 + 33
= 645

Mean = 645 / 13 ≈ 24.85

#### Calculating the median for Team 1:
To find the median, we first order the ages:
18, 18, 20, 22, 22, 22, 24, 24, 25, 28, 30, 33, 35

The median (middle value in an ordered list) for 13 values is the 7th value:
Median = 24

#### Calculating Q1 for Team 1:
Q1 is the median of the first half (lower 6 values):
18, 18, 20, 22, 22, 22

Median of these values = (20 + 22) / 2 = 21

### Team 2 Ages:
19, 20, 26, 28, 25, 29, 34, 37, 39, 32, 27, 26, 25

#### Calculating the mean for Team 2:
Sum = 19 + 20 + 26 + 28 + 25 + 29 + 34 + 37 + 39 + 32 + 27 + 26 + 25 = 19 + 20 + 26 + 28 + 25 + 29 + 34 + 37 + 39 + 32 + 27 + 26 + 25
= 503

Mean = 503 / 13 ≈ 27.0

#### Calculating the median for Team 2:
Ordered ages:
19, 20, 25, 25, 26, 26, 27, 28, 29, 32, 34, 37, 39

Median = 28 (7th value)

#### Calculating Q1 for Team 2:
Q1 is the median of the first half (lower 6 values):
19, 20, 25, 25, 26, 26

Median of these values = (25 + 25) / 2 = 25

### Summary of Results:
- **Mean of Team 1** ≈ 24.85
- **Mean of Team 2** ≈ 27.0
- **Median of Team 1** = 24
- **Median of Team 2** = 28
- **Q1 of Team 1** = 21
- **Q1 of Team 2** = 25

### True Statements:
- A: **False** (Mean of Team 2 is greater)
- B: **True** (Mean of Team 2 is greater)
- C: **False** (Median of Team 2 is greater)
- D: **False** (Q1 of Team 2 is greater)

The correct response is **B**: The mean for Team 2 is greater than the mean for Team 1.