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The mode of the following data is 67. Find the missing frequency x.

Class 40-50 50-60 60-70 70-80 80-90
Frequency 5 x 15 12 7

User Babul
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1 Answer

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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.

User StormKrow
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