There are three number cards. The numbers are hidden. The mode of the three numbers is 5. The mean of the three numbers is 8. What are the three numbers? Please show your working
2006-11-29 14:32:44 · 5 answers · asked by steven08zl 1 in Science & Mathematics ➔ Mathematics
The mode is the data point that appears the most often. From the problem statement, there's a single mode, 5. So, since there are 3 cards, then at least 2 of the cards must be 5. (If all 3 cards are different, then there would be 3 modes.)
So the cards are 5, 5, and x. (x could be 5 without changing the mode). Now, look at the mean. To find the mean, add up all the values, and divide by the number of values. So add 5 + 5 + x to get x + 10, and divide that by 3. That expression must equal 8.
So, you now have an equation to solve: (x + 10) / 3 = 8. Solve it as you normally would:
multiply both sides by 3 to get x + 10 = 24
subtract 10 from both sides to get x = 14.
So the 3 cards are 5, 5, and 14. The mode is 5, and the mean is (5 + 5 + 14) / 3 = 24 / 3 = 8.
2006-11-29 14:40:44 · answer #1 · answered by Kevin W 2 · 0⤊ 0⤋
If the mode is 5, that means that 5 is in the set more than any other number. That means that either two of the number cards show 5, or all three do.
All three can't show 5, because if they did, the mean would also be 5.
So two of the cards show 5, and the third shows an unknown number.
If the three numbers have mean 8, then they must sum to 24.
We have:
5 + 5 + x = 24
10 + x = 24
x = 14.
The cards must have 5, 5, and 14.
Check
The mode must be 5 because it is the most common number in the set.
The average of 5, 5, and 14 is:
(5 + 5 + 14)/3 = 24/3 = 8
It works!
2006-11-29 22:36:36 · answer #2 · answered by hokiejthweatt 3 · 0⤊ 0⤋
for the mode to be 5, five must appear twice. Set up an equation. (5+5+x ) all divided by three equals 8
multiply by three
5+5+x=24 subtract 10 from both sides
x=14
Check your work. 5, 5, 14. The mode is 5. The mean is 5+5+14= 24/3 = 8
2006-11-29 22:45:59 · answer #3 · answered by kyla m 1 · 0⤊ 0⤋
The mode is the number that occurs the most often.
Since there are only 3 numbers, 5 must be 2 of them...otherwise there wouldn't be a mode.
(5 + 5 + x)/3 = 8
10 + x = 24
x = 14
2006-11-29 22:37:28 · answer #4 · answered by Jim Burnell 6 · 0⤊ 0⤋
5+5+x=24
x=24-10
=14
2006-11-29 22:38:23 · answer #5 · answered by raj 7 · 0⤊ 0⤋