Question

The ages of randomly selected employees at two companies are recorded. Their ages are as follows:

company A: 34 28 36 37 30 42 52 39 38 45
company B: 29 32 51 49 33 36 45 43 44 51


Which of the following statements is true? Select all that apply.

(2 points)
Responses

The mean age of employees from Company A is higher than the mean age of employees from Company B.
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 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.

Answer 1

To determine which statements are true, let's calculate the mean, median, and range of the ages for both companies.

**Company A: Ages - 34, 28, 36, 37, 30, 42, 52, 39, 38, 45**

1. **Mean**:
\[
\text{Mean for Company A} = \frac{34 + 28 + 36 + 37 + 30 + 42 + 52 + 39 + 38 + 45}{10} = \frac{ 37 1/2}{10} = 38.5
\]

2. **Median**:
- Sorted ages: 28, 30, 34, 36, 37, 38, 39, 42, 45, 52
- Median is the average of the 5th and 6th values:
\[
\text{Median for Company A} = \frac{37 + 38}{2} = 37.5
\]

3. **Range**:
\[
\text{Range for Company A} = 52 - 28 = 24
\]

**Company B: Ages - 29, 32, 51, 49, 33, 36, 45, 43, 44, 51**

1. **Mean**:
\[
\text{Mean for Company B} = \frac{29 + 32 + 51 + 49 + 33 + 36 + 45 + 43 + 44 + 51}{10} = \frac{ 413 }{10} = 41.3
\]

2. **Median**:
- Sorted ages: 29, 32, 33, 36, 43, 44, 45, 49, 51, 51
- Median is the average of the 5th and 6th values:
\[
\text{Median for Company B} = \frac{43 + 44}{2} = 43.5
\]

3. **Range**:
\[
\text{Range for Company B} = 51 - 29 = 22
\]

**Comparisons**:
- Mean:
- Mean for Company A = 38.5
- Mean for Company B = 41.3
**Conclusion**: Mean of Company A is NOT higher than Company B.

- Median:
- Median for Company A = 37.5
- Median for Company B = 43.5
**Conclusion**: Median of Company A is lower than Company B.

- Range:
- Range for Company A = 24
- Range for Company B = 22
**Conclusion**: Range of Company A is higher than Company B.

**True Statements**:
1. The median age of employees from Company A is lower than the median age of employees from Company B.
2. The range of ages of employees from Company A is higher than the range of ages of employees from Company B.

So the true statements are:
- 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.