Answer :
The three numbers are 4, 5, and 12.
To find three numbers that satisfy these conditions, we can use the properties of mean, median, and range.
Let's denote the three numbers as x , y , and z . The median is the middle number when the numbers are arranged in ascending order. Since the median is 5, we have:
y = 5
The mean of the three numbers is given by:
[tex]\[ \text{Mean} = \frac{x + y + z}{3} \][/tex]
Since the mean is 7, we have:
[tex]\[ \frac{x + 5 + z}{3} = 7 \]\[ x + z = 21 - 5 \]\[ x + z = 16 \][/tex]
The range of the three numbers is the difference between the largest and smallest numbers. Since the range is 8, we have:
[tex]\[ \text{Range} = \text{Largest number} - \text{Smallest number} = z - x = 8 \][/tex]
Now, we have two equations:
1. x + z = 16
2. z - x = 8
We can solve these equations simultaneously to find the values of x and z .
Adding the two equations:
(x + z) + (z - x) = 16 + 8
2z = 24
z = 12
Substituting the value of z into the first equation:
x + 12 = 16
x = 4
So, the three numbers are 4, 5, and 12.
Question
What are the 3 numbers where the mean is 7 the median is 5 and range is 8?
