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The table gives the completion times of 130 males and 70 females in an 8K race. The question asks us to find the center (midpoint) of the class interval that contains the median of the completion times of the entire group (130 males + 70 females = 200 participants).

### Step 1: Combine the frequencies of males and females
We will first sum the frequencies for each class interval:

| Completion time (minutes) | Frequency Males | Frequency Females | Total Frequency |
|---------------------------|-----------------|-------------------|-----------------|
| [12 – 20]                 | 19              | 6                 | 25              |
| [20 – 28]                 | 14              | 8                 | 22              |
| [28 – 36]                 | 26              | 12                | 38              |
| [36 – 44]                 | 24              | 25                | 49              |
| [44 – 52]                 | 47              | 19                | 66              |

### Step 2: Find the median position
The total number of participants is 200, so the median will be at the position:
\[
\text{Median position} = \frac{200 + 1}{2} = 100.5
\]
Thus, the median will lie between the 100th and 101st participants.

### Step 3: Determine the cumulative frequency
We now calculate the cumulative frequency:

| Completion time (minutes) | Total Frequency | Cumulative Frequency |
|---------------------------|-----------------|-----------------------|
| [12 – 20]                 | 25              | 25                    |
| [20 – 28]                 | 22              | 47                    |
| [28 – 36]                 | 38              | 85                    |
| [36 – 44]                 | 49              | 134                   |
| [44 – 52]                 | 66              | 200                   |

From the cumulative frequency, we can see that the 100th and 101st participants fall within the class interval [36 – 44], because the cumulative frequency reaches 134 after this interval.

### Step 4: Find the midpoint of the class interval [36 – 44]
The midpoint of an interval is given by:
\[
\text{Midpoint} = \frac{\text{Lower bound} + \text{Upper bound}}{2} = \frac{36 + 44}{2} = 40
\]

Thus, the midpoint of the class interval containing the median is **40 minutes**.

Would you like more details, or do you have any other questions?

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Here are 5 related questions:
1. How do you find the median for a grouped frequency distribution?
2. What is the importance of cumulative frequency in finding the median?
3. How can we calculate the exact value of the median in grouped data, beyond just the interval?
4. How do we interpret the midpoint of a class interval in real-world data analysis?
5. How would the calculation change if there were an odd number of participants?

**Tip:** Always check whether the cumulative frequency crosses the median position when identifying the correct class interval for grouped data.

What is the center (midpoint) of the class interval that contains the median of the completion times of the whole group of males and females who participated in the race?

Learn how to find the midpoint of the class interval containing the median completion times of males and females who participated in an 8K race. The problem involves the median position, cumulative frequency, and class interval midpoint calculations.

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