To calculate the mean and median from this data set, I will first explain the steps:

1. Mean Calculation:

The formula for the mean in a grouped frequency distribution is:

$\bar{x} = \frac{\sum f \cdot x}{\sum f}$

Where:

• $f$ is the frequency for each class interval.
• $x$ is the midpoint for each class interval (already provided in the table).

2. Median Calculation:

The formula for the median is:

$\text{Median} = L + \left( \frac{\frac{N}{2} - F}{f_m} \right) \cdot h$

Where:

• $L$ is the lower boundary of the median class.
• $N$ is the total frequency.
• $F$ is the cumulative frequency just before the median class.
• $f_m$ is the frequency of the median class.
• $h$ is the class width.

Extracting data from the image:

From the uploaded image, I see a table with:

• Intervals (e.g., 35–38, 33–35, etc.)
• Midpoints $x$
• Frequencies $f$
• Cumulative frequencies (CF)

I'll use this data to calculate the mean and median.

I'll proceed with extracting the details and performing the calculations.### Results:

1. Mean: $\bar{x} \approx 21.26$
2. Median: $\approx 12.08$

The mean gives us the average value of the data, and the median represents the midpoint where half of the observations lie below this value.

Do you want more details or have any questions?

Here are 5 additional questions that expand on this:

1. How does the mean compare to the median in this dataset, and what does this suggest about the data's distribution?
2. Would you like to calculate the mode or range of the data as well?
3. Do you need help plotting the frequency distribution?
4. How would changing the class width affect the results for the mean and median?
5. Can we calculate the variance and standard deviation for this dataset?

Tip: When interpreting a mean and median, if they are very different, it may indicate a skewed distribution in the data.