Answer :
Final answer:
The mode of the given distribution is found within the class interval of 20-25, as this interval has the highest frequency of 75, marking it as the most frequently occurring range in the dataset.
Explanation:
The mode, in statistics, is defined as the value that appears most frequently in a set of data. For the provided distribution, the class intervals and frequencies are as follows: 10-15, 15-20, 20-25, 25-30, 30-35, and 35-40 with respective frequencies of 30, 45, 75, 35, 25, and 15.
Upon examination of the given frequencies, it is observed that the interval 20-25 has the highest frequency, which is 75. Hence, this interval represents the mode of the distribution since the mode is concerned with the frequency of occurrence within a dataset.
It's important to note that while we identify the modal interval, the exact value within that range declared as the mode can vary unless specified further.
In essence, the highest frequency signifies the mode in a frequency distribution, providing insight into the most common or popular range within a dataset. This concept is crucial in various statistical analyses and real-world applications, including market research, quality control, and decision-making processes.
