What is the median of the given data?
2, 3, 2, 3, 6, 5, 4, 7

Options

A. 4
B. `4.5`
C. `3.5`
D. 3

Answer

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

### Step 1: Arrange the Data in Ascending Order
The first step in finding the median is to arrange the data in ascending order.

Given data:
2, 3, 2, 3, 6, 5, 4, 7

Arranging this in ascending order:
2, 2, 3, 3, 4, 5, 6, 7

### Step 2: Determine the Number of Observations (n)
Next, we need to determine the number of observations in the data set.

Counting the numbers:
There are 8 numbers in total.

### Step 3: Check if n is Odd or Even
To find the median, we need to check if the number of observations (n) is odd or even.

Since n = 8, which is even, we will use the formula for the median of an even set of numbers.

### Step 4: Use the Median Formula for Even n
For an even number of observations, the median is calculated using the formula:
\[ \text{Median} = \frac{\text{(n/2)th term} + \text{(n/2 + 1)th term}}{2} \]

### Step 5: Calculate n/2 and n/2 + 1
Now, we calculate:
- \( n/2 = 8/2 = 4 \) (4th term)
- \( n/2 + 1 = 4 + 1 = 5 \) (5th term)

### Step 6: Identify the 4th and 5th Terms
From the arranged data:
- The 4th term is 3.
- The 5th term is 4.

### Step 7: Calculate the Median
Now we can substitute these values into the median formula:
\[ \text{Median} = \frac{3 + 4}{2} = \frac{7}{2} = 3.5 \]

### Final Answer
The median of the given data set is **3.5**.

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