Find the median for the following data :
` " 50 59 27 78 54 72"`
`" 58 57 31 65 42 60 "`
` " 22 37 40 and 28 " `

Answer

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

### Step 1: Organize the Data
First, we need to arrange the data in ascending order.

Given data:
```
50, 59, 27, 78, 54, 72, 58, 57, 31, 65, 42, 60, 22, 37, 40, 28
```

Arranging in ascending order:
```
22, 27, 28, 31, 37, 40, 42, 50, 54, 57, 58, 59, 60, 65, 72, 78
```

### Step 2: Count the Total Number of Observations
Next, we count the total number of observations in the data set.

Total observations = 16 (since there are 16 numbers in the arranged list).

### Step 3: Determine if the Number of Observations is Even or Odd
Since the total number of observations (16) is even, we will use the formula for finding the median in a data set with an even number of observations.

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

Here, \( n = 16 \).

Calculating:
- \( n/2 = 16/2 = 8 \)
- \( n/2 + 1 = 8 + 1 = 9 \)

### Step 5: Identify the 8th and 9th Terms
From the arranged data:
- 8th term = 50
- 9th term = 54

### Step 6: Calculate the Median
Now, substitute the values into the median formula:
\[ \text{Median} = \frac{50 + 54}{2} = \frac{104}{2} = 52 \]

### Conclusion
Therefore, the median of the given data set is **52**.

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