Find a set of six whole numbers that have a mean, a median, and a mode of 50. The numbers cannot all be the same.
In a normal distribution, mean = mode = median. Have either two or four numbers = 50, with the others spread individually and equidistant from 50 on both sides.
48, 49, 50, 50, 51, 52
To find a set of six whole numbers that have a mean, median, and mode of 50, we need to consider the properties of these statistical measures.
Mean: The mean is the average of a set of numbers. It is found by summing all the numbers and dividing by the total count. In this case, since we have six numbers, the sum of the numbers must be 6 * 50 = 300.
Median: The median is the middle value of a set of numbers when they are arranged in order. Since we have six numbers, the median will be the average of the two middle values. Therefore, two of the numbers must be the same and higher or equal to 50, while the other two numbers must be the same and lower or equal to 50.
Mode: The mode is the most frequently occurring value in a set of numbers. To have a mode of 50, we need at least two occurrences of 50 in the set.
With these considerations in mind, one possible set of numbers could be:
49, 49, 50, 50, 51, 53
Here's how we arrived at this set:
1. Start with the two middle numbers being the same, equal to 50.
2. To satisfy the mean condition, choose two numbers lower than 50 and two numbers higher than 50.
- We chose 49 and 49 for the numbers lower than 50 to keep the median intact.
- We chose 51 and 53 for the numbers higher than 50 to keep the median intact.
3. Finally, we have a set of six whole numbers with a mean, median, and mode of 50: 49, 49, 50, 50, 51, 53.