Answer:
First, we arrange the values in ascending order. Given that the data set has 9 values, the median represents the middle value when the values are arranged in order.
In this case, the least value is 8 and the greatest value is 20. To find the median, we need to determine the middle value. Since there are an odd number of values (9), the median will be the value at the (9 + 1) / 2 = 5th position.
Arranging the values in ascending order: 8, x, x, x, 11, x, x, x, 20
From the given information, we know that the median is 11. Therefore, the middle value must be 11.
Arranging the values again: 8, x, x, x, 11, x, x, x, 20
Since the median is the middle value, the remaining values can be any numbers as long as they are greater than or equal to 8 and less than or equal to 20. There is no unique solution for the remaining values in the data set, as long as the conditions are met.
Here are some possible data sets that satisfy the given conditions:
- 8, 9, 10, 11, 12, 13, 19, 20
- 8, 9, 10, 11, 12, 14, 16, 20
- 8, 9, 10, 11, 12, 15, 17, 20
There are many other possible data sets that satisfy the given conditions.