To solve the problem of determining the interquartile range (IQR) from the given histogram, we first need to identify the first quartile ($Q_1$) and the third quartile ($Q_3$).

Steps to Solve:

1. Count the total number of employees: The problem states there are 41 employees, and this is confirmed by counting the total frequency from the histogram.

2. Quartiles Calculation:

   • $Q_1$: The first quartile is the 25th percentile, meaning 25% of the 41 employees (approximately the 10th or 11th employee).
   • $Q_2$ (Median): The median is the 50th percentile, or approximately the 21st employee.
   • $Q_3$: The third quartile is the 75th percentile, meaning approximately the 31st employee.

3. Histogram Interpretation: From the histogram:

   • The number of employees for different ranges of hours is as follows:

     • 0-5 hours: 3 employees
     • 5-10 hours: 3 employees
     • 10-15 hours: 4 employees
     • 15-20 hours: 4 employees
     • 20-25 hours: 3 employees
     • 25-30 hours: 3 employees
     • 30-35 hours: 5 employees
     • 35-40 hours: 7 employees
     • 40-45 hours: 6 employees
     • 45-50 hours: 1 employee

   • The 10th-11th employee falls into the 10-15 hours range.

   • The 31st employee falls into the 35-40 hours range.

4. Interquartile Range (IQR):

   • $Q_1$ is around 12.5 hours (between 10 and 15 hours).
   • $Q_3$ is around 37.5 hours (between 35 and 40 hours).

   Therefore, the interquartile range is: $IQR = Q_3 - Q_1 = 37.5 - 12.5 = 25 \text{ hours}$

Closest Answer Choice:

Since the answer choices provided are:

• A) 15
• B) 19
• C) 27
• D) 31
• E) 32

The closest to our calculated interquartile range of 25 is C) 27.

Would you like further clarification or a deeper explanation?

Here are five related questions for further practice:

1. How do you calculate the median from a histogram?
2. What is the significance of the interquartile range in data analysis?
3. How would the interquartile range change if more employees worked 0-5 hours?
4. Can you calculate the exact values of Q1 and Q3 for this dataset?
5. How does the shape of the distribution affect the interquartile range?

Tip: The interquartile range is a robust measure of spread because it is less sensitive to extreme values compared to the range.