Given the information about the data set with 101 data points ranging between 0 and 200, and the fact that there are no values in the class 101 – 120, we can analyze the statements provided.
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All the data lies below 100.
- This statement is not necessarily true. It is entirely possible for there to be values from 0 to 200, but since there are no values in the 101-120 range, there could still be values in the ranges above 120. For example, if the highest value were 199, there still would be no values in the 101-120 range.
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The median could be in the range 101 – 120.
- This statement is false. Since there are no data points in the range of 101-120, the median, which is the middle value of the ordered data set, cannot fall in that range. The median would have to be from the existing ranges (specifically, below or equal to 100).
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The mean of the data will not be between 101 and 120.
- This statement is true. Since there are no data points in the 101-120 range, it is impossible for the mean to fall within that range. As the mean is influenced by all data points in the set, it too cannot occupy a value in that range due to the absence of data points there.
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The relative frequency of the class 101 – 120 is 0.
- This statement is true. Since there are no values falling into the class of 101-120, the relative frequency, which is the fraction of the total number of data points that fall into this class, will indeed be 0.
In summary:
- The correct evaluations for the statements are:
- False for "All the data lies below 100."
- False for "The median could be in the range 101 – 120."
- True for "The mean of the data will not be between 101 and 120."
- True for "The relative frequency of the class 101 – 120 is 0."