Make up a set of at least 12 numbers that has the following landmarks:
Minimum: 50
Maximum: 57
Median: 54
Mode: 56
The lowest number would be 50 and the highest is 57. That takes care of two scores. Since the mode is the most frequently occurring score, at least two scores will be 56. Still 8 scores remain.
Insert the remaining scores so half will ≤ median and half ≥ median, since the median = 50th percentile. You may have to add scores to the modal value.
To create a set of at least 12 numbers with the given landmarks, we need to ensure that the numbers fall within the given range and satisfy the conditions for minimum, maximum, median, and mode.
Here's one example of a set that meets the criteria:
56, 57, 56, 54, 53, 55, 56, 52, 51, 53, 50, 52
To explain how I arrived at this set:
1. Minimum: The minimum value provided is 50, so we need to include it in the set.
2. Maximum: The maximum value given is 57, so we need to include it in the set.
3. Median: The median refers to the middle value when the numbers are arranged in ascending order. Since the median is given as 54, we need to include it in the set.
4. Mode: The mode refers to the number that appears most frequently in the set. Since the mode is given as 56, we should include it multiple times. In this case, we included it three times.
The remaining numbers in the set can be arranged in any order, ensuring that they fall within the given range and don't disrupt the minimum, maximum, median, and mode conditions.
Please note that there can be multiple valid sets that fulfill these conditions, so the example provided above is just one possibility.