The median of the following data is
25,34,31,23,22,26,35,29,20,32

Options

A. 27.5
B. 29.5
C. 22.5
D. None of these

Answer

To find the median of the given data set, we will follow these steps:

### Step 1: Arrange the Data in Ascending Order
First, we need to sort the data set in ascending order. The given data is:
\[ 25, 34, 31, 23, 22, 26, 35, 29, 20, 32 \]

Arranging these values in ascending order, we get:
\[ 20, 22, 23, 25, 26, 29, 31, 32, 34, 35 \]

### Step 2: Count the Number of Observations
Next, we count the number of observations in the data set.
In this case, we have:
\[ 10 \text{ observations} \]

### Step 3: Determine if the Number of Observations is Even or Odd
Since we have 10 observations, which is an even number, we will use the formula for finding the median in an even data set.

### Step 4: Use the Median Formula for Even Observations
The formula for the median when the number of observations (n) is even is:
\[ \text{Median} = \frac{\text{n/2th term} + \text{(n/2 + 1)th term}}{2} \]
Here, \( n = 10 \).

Calculating \( n/2 \):
\[ n/2 = 10/2 = 5 \]
Thus, we need the 5th and 6th terms.

### Step 5: Identify the 5th and 6th Terms
From our ordered data set:
- The 5th term is \( 26 \)
- The 6th term is \( 29 \)

### Step 6: Calculate the Median
Now we can substitute these values into the median formula:
\[ \text{Median} = \frac{26 + 29}{2} = \frac{55}{2} = 27.5 \]

### Final Answer
Thus, the median of the given data set is:
\[ \text{Median} = 27.5 \]

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