Question

The ages of randomly selected employees at two companies are recorded. Their ages are as follows:
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.
statements 2 and 3
statements 1,2, and 3
statements 1 and 3
statements 1 and 2

Answer 1

Let's calculate the mean, median, and range of ages for both companies to evaluate the statements:

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

1. **Mean Age for Company A:**
\[
\text{Mean} = \frac{\text{Sum of Ages}}{\text{Number of Employees}} = \frac{34 + 28 + 36 + 27 + 45 + 44 + 30 + 42 + 41 + 40 + 50 + 48 + 52 + 45 + 39 + 38}{16}
\]
\[
= \frac{ 34 + 28 + 36 + 27 + 45 + 44 + 30 + 42 + 41 + 40 + 50 + 48 + 52 + 45 + 39 + 38 = 735}{16} \approx 45.94
\]

2. **Median Age for Company A:**
- 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.
\[
\text{Median} = \frac{40 + 41}{2} = 40.5
\]

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

---

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

1. **Mean Age for Company B:**
\[
\text{Mean} = \frac{29 + 32 + 48 + 51 + 49 + 37 + 33 + 35 + 36 + 40 + 45 + 48 + 43 + 43 + 44 + 48}{16}
\]
\[
= \frac{ 29 + 32 + 48 + 51 + 49 + 37 + 33 + 35 + 36 + 40 + 45 + 48 + 43 + 43 + 44 + 48 = 743}{16} \approx 46.44
\]

2. **Median Age for Company B:**
- 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.
\[
\text{Median} = \frac{43 + 43}{2} = 43
\]

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

---

**Now we can analyze the statements:**

1. **The mean age of employees from Company A is higher than the mean age of employees from Company B.**
- Company A: ≈ 45.94, Company B: ≈ 46.44. This statement is **false**.

2. **The median age of employees from Company A is lower than the median age of employees from Company B.**
- Company A: 40.5, Company B: 43. This statement is **true**.

3. **The range of ages of employees from Company A is higher than the range of ages of employees from Company B.**
- Company A: 25, Company B: 22. This statement is **true**.

---

Therefore, the true statements are statement 2 and statement 3.

**The correct option is: statements 2 and 3.**