Final answer:
To construct a data set where the median and mode are the same, ensure one of the values appears at least twice and is in the middle when ordered. An example is {8, 9, 10, 10, 11}, where both the median and mode are 10. The correct definition of median is the value in the middle of an ordered data set.
Step-by-step explanation:
Understanding Median and Mode
The median is a measure of central tendency that represents the middle value in a data set when the numbers are arranged in ascending order. In an odd-sized data set, it is simply the middle number; for an even-sized data set, it is the average of the two middle numbers. The mode is another measure of central tendency, indicating the most frequently occurring number(s) in the data set.
To construct a data set where the median and the mode are the same, consider the values {8, 9, 10, 10, 11}. Here, both the median and mode are 10. The data entries are not all the same, fulfilling the given criteria.
Now, let's clarify the options provided regarding the definition of median:
- A describes the mean (average), not the median.
- B is the correct definition of median.
- C defines the mode.
- D refers to an outlier, which is unrelated to median.