The data below shows the number of batsmen having different batting averages.
`{:("Average"," Number of batsmen"),(40-44," "12),(44-48," "10),(48-52," "8),(52-56," "6),(56-60," "4):}`
What is the mean batting average per batsman ?

Options

A. 46
B. 45
C. 48
D. 47

Answer

To find the mean batting average per batsman, we will follow these steps:

### Step 1: Identify the midpoints of each batting average range.
The midpoints can be calculated as follows:
- For the range 40-44: Midpoint = (40 + 44) / 2 = 42
- For the range 44-48: Midpoint = (44 + 48) / 2 = 46
- For the range 48-52: Midpoint = (48 + 52) / 2 = 50
- For the range 52-56: Midpoint = (52 + 56) / 2 = 54
- For the range 56-60: Midpoint = (56 + 60) / 2 = 58

### Step 2: Multiply each midpoint by the corresponding number of batsmen.
- For 40-44: 42 * 12 = 504
- For 44-48: 46 * 10 = 460
- For 48-52: 50 * 8 = 400
- For 52-56: 54 * 6 = 324
- For 56-60: 58 * 4 = 232

### Step 3: Calculate the total of all the products obtained in Step 2.
Total = 504 + 460 + 400 + 324 + 232 = 1920

### Step 4: Calculate the total number of batsmen.
Total number of batsmen = 12 + 10 + 8 + 6 + 4 = 40

### Step 5: Calculate the mean batting average.
Mean batting average = Total of products / Total number of batsmen = 1920 / 40 = 48

### Final Answer:
The mean batting average per batsman is **48**.

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