To find the median of the given data, I'll analyze the data in the image step-by-step:

Data from the table:

There are two columns:

1. X values: 6, 5, 3, 7, 4, 9
2. F values (frequencies): 4, 5, 8, 2, 14, 11

Steps to find the median:

1. Expand the dataset: Multiply each X value by its frequency (F) to create the full data set.

   • For X = 6, F = 4 → 6 appears 4 times: [6, 6, 6, 6]
   • For X = 5, F = 5 → 5 appears 5 times: [5, 5, 5, 5, 5]
   • For X = 3, F = 8 → 3 appears 8 times: [3, 3, 3, 3, 3, 3, 3, 3]
   • For X = 7, F = 2 → 7 appears 2 times: [7, 7]
   • For X = 4, F = 14 → 4 appears 14 times: [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4]
   • For X = 9, F = 11 → 9 appears 11 times: [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]

2. Total frequency: Add all frequencies: $4 + 5 + 8 + 2 + 14 + 11 = 44$.

3. Sort the dataset: Combine all values into a single sorted dataset: $[3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]$

4. Find the position of the median: Since the total number of observations ($N = 44$) is even, the median is the average of the 22nd and 23rd values.

5. Locate the 22nd and 23rd values:

   • The first 8 values are 3.
   • The next 14 values (positions 9 to 22) are 4.
   • The 22nd value is 4, and the 23rd value (starting the next set) is 5.

6. Calculate the median: Median = $\frac{4 + 5}{2} = 4.5$.

Final Answer:

The median of the given data is 4.5.

Let me know if you'd like more explanation or additional questions solved! Here are related follow-ups:

1. How do you calculate the mode for the same dataset?
2. Can you explain the difference between mean, median, and mode?
3. How would the median change if the highest frequency shifted?
4. What is the significance of an even vs. odd total frequency for the median?
5. Can you graph the frequency distribution for this data?

Tip: Sorting and organizing your data carefully ensures accurate statistical calculations.