The Median of the following discrete series is
`{:(x_(i),3,6,5,8,12,7),(f_(i)"",5,2,4,6,7,6):}`

Options

A. 7
B. 8
C. 9
D. 6

Explanation

To find the median of the given discrete series, we will follow these steps:

### Step 1: Arrange the data in increasing order
The given data is:
- \( x_i = \{3, 5, 6, 7, 8, 12\} \)
- \( f_i = \{5, 2, 4, 6, 7, 6\} \)

Arranging \( x_i \) in increasing order:
- \( x_i = 3, 5, 6, 7, 8, 12 \)

### Step 2: Write the corresponding frequencies
Corresponding frequencies for each \( x_i \):
- \( f_i = 5, 2, 4, 6, 7, 6 \)

### Step 3: Calculate the cumulative frequency
We will calculate the cumulative frequency for each \( x_i \):
- For \( x_i = 3 \): Cumulative frequency = \( 5 \)
- For \( x_i = 5 \): Cumulative frequency = \( 5 + 2 = 7 \)
- For \( x_i = 6 \): Cumulative frequency = \( 7 + 4 = 11 \)
- For \( x_i = 7 \): Cumulative frequency = \( 11 + 6 = 17 \)
- For \( x_i = 8 \): Cumulative frequency = \( 17 + 7 = 24 \)
- For \( x_i = 12 \): Cumulative frequency = \( 24 + 6 = 30 \)

So, the cumulative frequencies are:
- \( 5, 7, 11, 17, 24, 30 \)

### Step 4: Calculate the total frequency (n)
Now, we will calculate the total frequency \( n \):
\[ n = 5 + 2 + 4 + 6 + 7 + 6 = 30 \]

### Step 5: Calculate \( n/2 \)
Next, we calculate \( n/2 \):
\[ n/2 = 30/2 = 15 \]

### Step 6: Find the median
To find the median, we need to identify the cumulative frequency that is just greater than \( n/2 \):
- The cumulative frequencies are \( 5, 7, 11, 17, 24, 30 \)
- The first cumulative frequency greater than \( 15 \) is \( 17 \), which corresponds to \( x_i = 7 \).

Thus, the median of the discrete series is:
\[ \text{Median} = 7 \]

### Summary of the solution:
The median of the given discrete series is \( 7 \).

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