To calculate the mean (rataan) of the students' body weights from the given histogram, we will follow these steps:

1. Identify the class intervals: Based on the x-axis labels, the class intervals are:

   • 40.5–49.5
   • 49.5–54.5
   • 54.5–59.5
   • 59.5–64.5
   • 64.5–69.5
   • 69.5–74.5

2. Identify the frequencies: These can be read from the heights of the histogram bars.

   • First class (40.5–49.5): 4 students
   • Second class (49.5–54.5): 6 students
   • Third class (54.5–59.5): 8 students
   • Fourth class (59.5–64.5): 10 students
   • Fifth class (64.5–69.5): 6 students
   • Sixth class (69.5–74.5): 4 students

3. Determine the midpoints of the class intervals: $\text{Midpoint} = \frac{\text{Lower bound} + \text{Upper bound}}{2}$

   • For 40.5–49.5: Midpoint = $(40.5 + 49.5) / 2 = 45$
   • For 49.5–54.5: Midpoint = $(49.5 + 54.5) / 2 = 52$
   • For 54.5–59.5: Midpoint = $(54.5 + 59.5) / 2 = 57$
   • For 59.5–64.5: Midpoint = $(59.5 + 64.5) / 2 = 62$
   • For 64.5–69.5: Midpoint = $(64.5 + 69.5) / 2 = 67$
   • For 69.5–74.5: Midpoint = $(69.5 + 74.5) / 2 = 72$

4. Calculate the weighted sum of the midpoints: We will multiply each midpoint by its frequency and sum these products.

$\text{Sum of midpoints} = (45 \times 4) + (52 \times 6) + (57 \times 8) + (62 \times 10) + (67 \times 6) + (72 \times 4)$

5. Sum the frequencies: This is the total number of students.

6. Calculate the mean: The mean weight is the total weighted sum of the midpoints divided by the total number of students.

Let's calculate this now.The mean (rataan) weight of the students is approximately 59.42 kg, which is closest to 59 kg.

Thus, the correct answer is:

a. 59 kg

Would you like more details or explanations about this process? Here are five related questions to explore further:

1. How are class intervals used in statistics for summarizing data?
2. What is the significance of midpoints in histogram analysis?
3. How do you calculate the mode from a histogram?
4. What are the differences between mean, median, and mode in statistics?
5. How can outliers affect the mean in a data set?

Tip: When calculating a mean from a histogram, ensure you correctly identify the midpoints and frequencies, as small mistakes can significantly affect the final result.