The data given below shows number of sixes and the number of batsmen who have hit them.
`{:("Number of sixes","Number of batsmen"),(1,2),(2,3),(3,1),(4,3),(5,2):}`
What is the median of number of sixes ?

Options

A. A) 5
B. B) 3
C. C) 4
D. D) `4.5`

Answer

To find the median of the number of sixes hit by batsmen, we can follow these steps:

### Step 1: Organize the Data
The data given is:
- Number of sixes: 1, 2, 3, 4, 5
- Number of batsmen: 2, 3, 1, 3, 2

We can interpret this as:
- 2 batsmen hit 1 six
- 3 batsmen hit 2 sixes
- 1 batsman hit 3 sixes
- 3 batsmen hit 4 sixes
- 2 batsmen hit 5 sixes

### Step 2: Create a Frequency List
Now, we can create a frequency list of the number of sixes:
- 1 six: 2 batsmen
- 2 sixes: 3 batsmen
- 3 sixes: 1 batsman
- 4 sixes: 3 batsmen
- 5 sixes: 2 batsmen

### Step 3: List All Values
Next, we will list all the values of sixes based on the number of batsmen:
- 1, 1 (for 2 batsmen hitting 1 six)
- 2, 2, 2 (for 3 batsmen hitting 2 sixes)
- 3 (for 1 batsman hitting 3 sixes)
- 4, 4, 4 (for 3 batsmen hitting 4 sixes)
- 5, 5 (for 2 batsmen hitting 5 sixes)

So, the complete list of sixes is:
1, 1, 2, 2, 2, 3, 4, 4, 4, 5, 5

### Step 4: Count the Total Number of Values
Now, we count the total number of values:
- Total values = 2 + 3 + 1 + 3 + 2 = 11

### Step 5: Calculate the Median Position
Since we have an odd number of values (11), the median is the value at the position given by the formula:
\[ \text{Median Position} = \frac{n + 1}{2} \]
Where \( n \) is the total number of values. Thus:
\[ \text{Median Position} = \frac{11 + 1}{2} = \frac{12}{2} = 6 \]

### Step 6: Find the Median Value
Now, we find the 6th value in the ordered list:
1, 1, 2, 2, 2, **3**, 4, 4, 4, 5, 5

The 6th value is **3**.

### Conclusion
Thus, the median number of sixes is **3**.