Question

Company A: 34, 28, 36, 27, 45, 44, 30, 42, 41, 40, 50, 48, 52, 45, 39, 38
Company B: 29, 32, 48, 51, 49, 37, 33, 35, 36, 40, 45, 48, 43, 43, 44, 48

Which of the following statements is true?

The mean age of employees from Company A is higher than the mean age of employees from Company B.
The median age of employees from Company A is lower than the median age of employees from Company B.
The range of ages of employees from Company A is higher than the range of ages of employees from Company B.

(1 point)
Responses
A. statements 1 and 3
B. statements 2 and 3
C. statements 1, 2, and 3
D.statements 1 and 2

Answer 1

To determine the truth of the statements, we need to calculate the mean, median, and range of ages for both Company A and Company B.

**Company A:**
Ages: 34, 28, 36, 27, 45, 44, 30, 42, 41, 40, 50, 48, 52, 45, 39, 38

1. **Mean**:
\[
\text{Mean} = \frac{\text{Sum of ages}}{\text{Number of ages}} = \frac{34 + 28 + 36 + 27 + 45 + 44 + 30 + 42 + 41 + 40 + 50 + 48 + 52 + 45 + 39 + 38}{16}
\]
\[
= \frac{696}{16} \approx 43.5
\]

2. **Median**:
- Sort the ages: 27, 28, 30, 34, 36, 38, 39, 40, 41, 42, 44, 45, 45, 48, 50, 52
- Median (average of the 8th and 9th values) = \(\frac{40 + 41}{2} = 40.5\)

3. **Range**:
\[
\text{Range} = \text{Max} - \text{Min} = 52 - 27 = 25
\]

**Company B:**
Ages: 29, 32, 48, 51, 49, 37, 33, 35, 36, 40, 45, 48, 43, 43, 44, 48

1. **Mean**:
\[
\text{Mean} = \frac{29 + 32 + 48 + 51 + 49 + 37 + 33 + 35 + 36 + 40 + 45 + 48 + 43 + 43 + 44 + 48}{16}
\]
\[
= \frac{776}{16} = 48.5
\]

2. **Median**:
- Sort the ages: 29, 32, 33, 35, 36, 37, 40, 43, 43, 44, 45, 48, 48, 48, 49, 51
- Median (average of the 8th and 9th values) = \(\frac{43 + 43}{2} = 43\)

3. **Range**:
\[
\text{Range} = \text{Max} - \text{Min} = 51 - 29 = 22
\]

**Comparison of Statistics:**

1. **Mean Age**:
- Company A: 43.5
- Company B: 48.5
- **False**: The mean age of employees from Company A is NOT higher than from Company B.

2. **Median Age**:
- Company A: 40.5
- Company B: 43
- **True**: The median age of employees from Company A is lower than from Company B.

3. **Range of Ages**:
- Company A: 25
- Company B: 22
- **True**: The range of ages of employees from Company A is higher than for Company B.

**Final assessment of the statements**:
- Statement 1: False
- Statement 2: True
- Statement 3: True

Thus, the correct answer is:
**B. statements 2 and 3**.