Final answer:
The frequency x for the class interval 50-60 is unknown and cannot be uniquely determined without additional information. However, to maintain 67 as the mode in the frequency distribution, x must be less than 15, as the mode's class interval must have the highest frequency.
Step-by-step explanation:
The student has provided a frequency distribution for a data set with a missing frequency value, denoted as x. We are told that the mode of this data set is 67, which falls within the class interval of 60-70. Since the mode is the value that appears most frequently, the class interval containing the mode must have the highest frequency.
We can see from the given data that:
- Class 40-50 has a frequency of 5
- Class 60-70 has a frequency of 15
- Class 70-80 has a frequency of 12
- Class 80-90 has a frequency of 7
To find the missing frequency, x, for the class interval 50-60, we can ascertain that x must be less than 15 since 15 is the frequency of the modal class 60-70. Therefore, x can be any value such that x < 15.
In the context of the provided question, x is not uniquely determined without additional information, but we understand that for the mode to be in the 60-70 range, x must be less than 15.