Median of a distribution is the value of the variable which divides it into equal parts . In case of individual observations `x_1,x_2` .. `x_n`, if the number of observations is odd, then median is the value of `((n+1)/2)` th observation when the observations have been arranged in ascending or descending order of magnitude. In case of even number of observations median is the A.M. of the values of `(n/2)`th and `(n/2+1)` th observations, arranged in ascending or descending order of magnitude . The mode of distribution is that value of the variable for which the frequency is maximum .
Median of the distribution 8,5,7,9,13,11,20,23 , 25 ,28 , 27 is

Options

A. (a)11
B. (b)13
C. (c)12
D. (d)20

Answer

To find the median of the given distribution of numbers \(8, 5, 7, 9, 13, 11, 20, 23, 25, 28, 27\), we will follow these steps:

### Step 1: Arrange the Observations in Ascending Order
First, we need to arrange the given observations in ascending order:
- The original numbers are: \(8, 5, 7, 9, 13, 11, 20, 23, 25, 28, 27\).
- Arranging them in ascending order gives us: \(5, 7, 8, 9, 11, 13, 20, 23, 25, 27, 28\).

### Step 2: Count the Number of Observations
Next, we count the total number of observations:
- The arranged list has 11 numbers: \(5, 7, 8, 9, 11, 13, 20, 23, 25, 27, 28\).
- Therefore, \(n = 11\).

### Step 3: Determine if \(n\) is Odd or Even
Since \(n = 11\) is odd, we will use the formula for the median for an odd number of observations:
- The median is the \(\left(\frac{n + 1}{2}\right)\)th observation.

### Step 4: Calculate the Position of the Median
Now, we calculate the position of the median:
\[ \text{Position} = \frac{n + 1}{2} = \frac{11 + 1}{2} = \frac{12}{2} = 6 \]
This means the median is the 6th observation in the ordered list.

### Step 5: Identify the Median Value
Now, we find the 6th observation in the arranged list:
- The arranged list is: \(5, 7, 8, 9, 11, 13, 20, 23, 25, 27, 28\).
- The 6th observation is \(13\).

### Final Answer
Thus, the median of the distribution is \(13\).

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