Given the following frequency distribution, which class interval contains the median value? Class Intervals: $10-19$ (frequency: $3$), $20-29$ (frequency: $7$), $30-39$ (frequency: $12$), $40-49$ (frequency: $8$), $50-59$ (frequency: $5$).

• A. $20-29$
• B. $30-39$
• C. $40-49$
• D. $50-59$

Answer: (B)

Verified step by step guidance

1. First, calculate the total number of observations by summing all the frequencies: \$3 + 7 + 12 + 8 + 5$.
2. Next, find the median position using the formula for the median in a frequency distribution: \(\frac{N + 1}{2}\), where \(N\) is the total number of observations.
3. Create a cumulative frequency table by adding frequencies successively: start with the first class frequency, then add the second class frequency to it, and so on.
4. Locate the class interval where the cumulative frequency is equal to or just exceeds the median position found in step 2. This class interval contains the median value.
5. Identify and state the class interval corresponding to this cumulative frequency as the median class.