To answer this question, let's break down each statement and verify them based on the given data.
### 1. The median could be in the range [tex]\(81-90\)[/tex].
The median is the value that separates the higher half from the lower half of the data set. For 98 data points, the median would be the average of the 49th and 50th data points when all values are arranged in order. Since we know that the class [tex]\(81-90\)[/tex] contains no data points (it is empty), the 49th and 50th data points cannot possibly fall into this range.
Conclusion: The median cannot be in the range [tex]\(81-90\)[/tex].
### 2. All the data lies below 80.
Given the information that there are 98 data points and no points in the [tex]\(81-90\)[/tex] class, this does not necessarily mean that all data points lie below 80. The data points could extend beyond 90 and proceed up to 160 as stated, but we only know that there is a gap in the range [tex]\(81-90\)[/tex].
Conclusion: It is not confirmed that all data lies below 80. Therefore, this statement is false.
### 3. The mean of the data will not be between [tex]\(81-90\)[/tex].
The mean of a set of data is the sum of all the values divided by the number of values. Since there are no data points at all in the [tex]\(81-90\)[/tex] range, the mean value, which is an average, cannot lie within this empty class. There simply aren’t any values in this range to contribute to the average.
Conclusion: The mean cannot be in the range [tex]\(81-90\)[/tex].
### 4. The relative frequency of the class [tex]\(81-90\)[/tex] is 0.
Relative frequency is calculated as the number of data points in a given class divided by the total number of data points. Given that there are no data points in the [tex]\(81-90\)[/tex] class:
[tex]\[ \text{Relative frequency} = \frac{\text{Number of data points in class 81-90}}{\text{Total number of data points}} = \frac{0}{98} = 0 \][/tex]
Conclusion: The relative frequency of the class [tex]\(81-90\)[/tex] is 0.
### Summarized Findings:
1. The median cannot be in the range [tex]\(81-90\)[/tex].
2. Not all the data lies below 80.
3. The mean of the data will not be between [tex]\(81-90\)[/tex].
4. The relative frequency of the class [tex]\(81-90\)[/tex] is 0.
Thus, the detailed step-by-step solution confirms:
- The median cannot be in the 81-90 range.
- Not all the data lies below 80.
- The mean cannot be in the 81-90 range.
- The relative frequency of the 81-90 range is 0.
