Final answer:
The mean of the data set is 29, the median is the third value which is 31, and the range is the difference between the smallest and largest values, which is 41.
Step-by-step explanation:
In order to calculate the mean, median, and range of the data set 31, 41, 47, 20, 6, we need to perform a few steps. First, let's organize the data in ascending order: 6, 20, 31, 41, 47.
Mean Calculation
The mean is the average of all numbers. We sum up all the values and divide by their count:
(6 + 20 + 31 + 41 + 47) / 5 = 145 / 5 = 29
Therefore, the mean of the data set is 29.
Median Calculation
The median is the middle value of an ordered data set. Since we have five numbers, the third number is the median:
Median = 31
The data set contains an odd number of values, so the median is simply the middle value.
Range Calculation
The range is the difference between the maximum and minimum values in the set:
Range = 47 - 6 = 41
Therefore, the range of the data set is 41.