https://file.aiquickdraw.com/mathbot/file/1729587805836sxc0o054.jpg

To calculate the median for grouped data, we need to follow these steps based on the data in the image:

### Step 1: Identify the relevant columns
From the image, we have the following intervals and corresponding frequencies:

| Class Interval  | Frequency (f) |
|-----------------|---------------|
| 10-19           | 2             |
| 20-29           | 7             |
| 30-39           | 14            |
| 40-49           | 17.8          |
| 50-59           | 13            |
| 60-69           | 8             |
| 70-79           | 5             |
| 80-89           | 3             |
| 90-99           | 2             |

### Step 2: Calculate cumulative frequency
Cumulative frequency (CF) is the running total of frequencies up to each class.

| Class Interval  | Frequency (f) | Cumulative Frequency (CF) |
|-----------------|---------------|---------------------------|
| 10-19           | 2             | 2                         |
| 20-29           | 7             | 9                         |
| 30-39           | 14            | 23                        |
| 40-49           | 17.8          | 40.8                      |
| 50-59           | 13            | 53.8                      |
| 60-69           | 8             | 61.8                      |
| 70-79           | 5             | 66.8                      |
| 80-89           | 3             | 69.8                      |
| 90-99           | 2             | 71.8                      |

### Step 3: Determine the median class
To find the median, we first need to compute the total frequency (N):
\[
N = 71.8
\]
The median class is the class where the cumulative frequency exceeds \(N/2 = 71.8 / 2 = 35.9\).

The median class is \(40-49\) because the cumulative frequency becomes 40.8 in this interval, which is the first cumulative frequency greater than 35.9.

### Step 4: Apply the median formula
The formula for the median of grouped data is:
\[
\text{Median} = L + \left( \frac{\frac{N}{2} - F}{f_m} \right) \times h
\]
Where:
- \(L\) = lower boundary of the median class = 40
- \(N/2 = 35.9\)
- \(F\) = cumulative frequency of the class before the median class = 23
- \(f_m\) = frequency of the median class = 17.8
- \(h\) = class width = 10 (since the class intervals are consistent)

### Step 5: Calculate the median
Substitute the values into the formula:
\[
\text{Median} = 40 + \left( \frac{35.9 - 23}{17.8} \right) \times 10
\]
\[
\text{Median} = 40 + \left( \frac{12.9}{17.8} \right) \times 10
\]
\[
\text{Median} = 40 + (0.7247 \times 10)
\]
\[
\text{Median} = 40 + 7.247
\]
\[
\text{Median} \approx 47.25
\]

Thus, the median is approximately **47.25**.

Would you like any additional details or explanations?

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Here are 5 related questions:
1. How do you calculate the mode for grouped data?
2. What is the difference between median and mean in grouped data?
3. How do you find the mean for grouped data from a frequency table?
4. Can the class width vary across different intervals when finding the median?
5. How is the median useful in data analysis compared to other measures of central tendency?

**Tip:** Always check if the class intervals are consistent when using formulas for grouped data.

Learn how to calculate the median for grouped data using the formula. This problem involves finding cumulative frequency, identifying the median class, and applying the median formula for grouped data. Suitable for students in Grades 9-12.

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