Final answer:
To find the mode of the data, calculate the frequency for each interval by dividing the number of batsmen by the number of runs scored. The interval with the highest frequency is the mode. The mode of the data is 3000-4000. The interval with the highest frequency is 3000-4000, which means the mode of the data is 3000-4000. Therefore, the correct option is a. 4608.695652.
Step-by-step explanation:
To find the mode of the data, we need to identify the value that appears most frequently. From the given distribution, we can see that the range of runs scored is divided into intervals, each corresponding to a certain number of batsmen. We can calculate the frequency for each interval by dividing the number of batsmen by the number of runs scored. The interval with the highest frequency will be the mode. Let's calculate the frequencies for each interval:
3000-4000: 44 batsmen/1000 runs = 0.044 batsmen/run
4000-5000: 18 batsmen/1000 runs = 0.018 batsmen/run
5000-6000: 9 batsmen/1000 runs = 0.009 batsmen/run
6000-7000: 7 batsmen/1000 runs = 0.007 batsmen/run
7000-8000: 6 batsmen/1000 runs = 0.006 batsmen/run
8000-9000: 3 batsmen/1000 runs = 0.003 batsmen/run
9000-10000: 1 batsman/1000 runs = 0.001 batsman/run
10000-11000: 1 batsman/1000 runs = 0.001 batsman/run
The interval with the highest frequency is 3000-4000, which means the mode of the data is 3000-4000. Therefore, the correct option is a. 4608.695652.