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 information provided about the highest value, lowest value, mean, and standard deviation.
First, we can calculate the range of the numbers by subtracting the lowest value from the highest value: Range = Highest Value - Lowest Value = 91 - 34 = 57.
Next, we can use the standard deviation to determine the spread of the numbers around the mean. Since the standard deviation is 5, we know that most of the values will fall within 5 units above and below the mean.
Given that the mean is 60, we can start by assigning a value of 60 to one of the numbers. From there, we can add or subtract the standard deviation until we reach the limits of the range.
Let's begin by arranging the numbers in ascending order:
34, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, 91
Here, "x" represents the unknown numbers.
To distribute the remaining 5 units above and below the mean, we divide them equally among the numbers. Since there are 19 remaining numbers to fill, each number will be adjusted by 5/19 units.
Starting from the mean (60), we can distribute the remaining 5 units above and below, alternating between adding and subtracting based on the position of the number in the sequence.
Using this process, we can calculate the values for each number:
34, 56.68, 59.36, 62.04, 64.72, 67.4, 70.08, 72.76, 75.44, 78.12, 80.8, 83.48, 86.16, 88.84, 91
Therefore, the 20 numbers, arranged in ascending order, are:
34, 56.68, 59.36, 62.04, 64.72, 67.4, 70.08, 72.76, 75.44, 78.12, 80.8, 83.48, 86.16, 88.84, 91