In 1919, W. Rhodes, the Yorkshire cricketer, scored 891 runs for his county at an average of 34.27; in 1920, he scored 949 runs at an average of 28.75; in 1921, 1329 runs at an average of 42.87 and in 1922, 1101 runs at an average of 36.70. What was his county batting average for the four years?

Options

A. 36.23
B. 37.81
C. 35.66
D. 28.72

Answer

To find W. Rhodes' county batting average over the four years, we need to follow these steps:

### Step 1: Identify the runs scored and averages for each year.
- 1919: Runs = 891, Average = 34.27
- 1920: Runs = 949, Average = 28.75
- 1921: Runs = 1329, Average = 42.87
- 1922: Runs = 1101, Average = 36.70

### Step 2: Calculate the total runs scored over the four years.
Total Runs = Runs in 1919 + Runs in 1920 + Runs in 1921 + Runs in 1922
Total Runs = 891 + 949 + 1329 + 1101

Calculating this gives:
Total Runs = 891 + 949 + 1329 + 1101 = 4270

### Step 3: Calculate the total number of innings played.
To find the total number of innings, we can use the average formula:
Average = Total Runs / Total Innings
From the averages given, we can derive the total innings for each year.

For each year, we can rearrange the average formula to find the number of innings:
Total Innings = Total Runs / Average

Calculating the total innings for each year:
- 1919: Innings = 891 / 34.27 ≈ 26
- 1920: Innings = 949 / 28.75 ≈ 33
- 1921: Innings = 1329 / 42.87 ≈ 31
- 1922: Innings = 1101 / 36.70 ≈ 30

Now, we sum these innings:
Total Innings = 26 + 33 + 31 + 30 = 120

### Step 4: Calculate the overall batting average.
Overall Average = Total Runs / Total Innings
Overall Average = 4270 / 120

Calculating this gives:
Overall Average = 35.5833 (approximately)

### Step 5: Round the average to two decimal places.
Rounding 35.5833 to two decimal places gives us 35.58.

### Final Answer:
W. Rhodes' county batting average for the four years is approximately **35.58**.

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