I am a set of 5 whole numbers that are less than 30. My median is 10. My range is 15. My mode is 10. The smallest number in my set is 10. My mean is 14. What are my numbers?
list the values in ascending order:
x x x x x
median: 10 (middle value is 10)
x x 10 x x
smallest: 10 (first value is 10)
10 x 10 x x
mode=10: (no new values possible between smallest and median, which are the same)
10 10 10 x x
range: 15
10 10 10 x 25
mean: 14 (means sum = 70)
10 10 10 15 25
To find the numbers that satisfy all the given conditions, we can follow these steps:
Step 1: Start with the smallest number, which is 10.
Step 2: Since the median is 10, we need two numbers smaller than 10 and two numbers larger than 10 to maintain the median of 10.
Step 3: The range (the difference between the largest and smallest numbers) is given as 15. Since the smallest number is 10, the largest number must be 10 + 15 = 25.
Step 4: Now we have the smallest and largest numbers in our set, which are 10 and 25, respectively.
Step 5: The mode is also given as 10, which means one more number in the set must be 10.
Step 6: We know that the mean is 14, which is the average of all five numbers. So, we can find the sum of all five numbers and subtract the known numbers to find the fifth missing number.
Let's calculate:
Mean = (Sum of all five numbers) / 5
14 = (10 + 10 + x + y + 25) / 5
14 = (45 + x + y) / 5
14 * 5 = 45 + x + y
70 = 45 + x + y
x + y = 70 - 45
x + y = 25
We have two equations now: x + y = 25 and x = y = 10.
Solving these equations simultaneously, we can find the values of x and y.
From equation x + y = 25:
10 + y = 25
y = 25 - 10
y = 15
So, we have x = y = 10 and y = 15.
Therefore, the set of numbers that satisfy all the given conditions is {10, 10, 10, 15, 25}.