There are 20 numbers, the highest is 91, the lowest is 34. The mean is 60 and the standard deviation is 5. What are the 20 numbers?
To find the 20 numbers, we need to use the given information about the mean and standard deviation.
The mean of a set of numbers is the sum of all the numbers divided by the total count of numbers. In this case, the mean is given as 60, which means we need to find the sum of the 20 numbers and then divide it by 20. So, the sum of the 20 numbers will be 60 multiplied by 20, which equals 1200.
The standard deviation measures the spread or dispersion of the numbers in the set. Without additional information, we cannot determine the exact position of each number within the set. However, we can assume that the numbers are approximately normally distributed around the mean. In a normal distribution, about 68% of the numbers fall within one standard deviation of the mean, about 95% within two standard deviations, and about 99.7% within three standard deviations.
Since the standard deviation is given as 5, we can assume that most of the numbers will fall within a range of 55 to 65 (i.e., mean ± 1 standard deviation). However, it is important to note that without further information or constraints, there can be multiple combinations of numbers that satisfy these conditions.
So, while we cannot determine the exact 20 numbers without more information, we can assume that any combination of 20 numbers with a mean of 60 and a standard deviation of 5, while having the highest number as 91 and the lowest number as 34, would be a valid answer.