Question 831094: four integers are added to a group of integers 3,4,5,5 and 8 and the mean, median and mode are increased by 1 each. what is the greatest integer in the new group of integers
Answer by JulietG(1812)   (Show Source):
You can put this solution on YOUR website! Existing integers: 3,4,5,5,8
Mean for those integers = 25/5 = 5
Mode for those integers = 5 (occurring most often)
Median for those integers = 5 (which number in the middle?)
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Where we want to be is:
Mean = (25 + A,B,C,D)/9 = 6
Mode = 6
Median = 6
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What helps most here is the mode. Since 5 occurs twice, 6 will necessarily have to be 3 of the remaining numbers. Now all we have to figure out is the 4th one.
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Knowing that 3 of the new numbers are 6, here's what we then have:
Mean = (43 + D)/9 = 6 [43 is 25 +6+6+6]
We can find the fourth number with this equation.
Let's multiply each side by 9 to get rid of that pesky fraction
43+D = 6*9
43+D = 54
subtract 43 from each side to get
D = 11
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Let's put out new four numbers in to make certain they're correct: 6,6,6,11
New set: 3,4,5,5,6,6,6,8,11
Mean = total values divided by number of values. 3+4+5+5+6+6+6+8+11 = 54. 54/9 = 6
Median -- which number is in the middle? 6
Mode -- which number occurs most often? 6
Success!
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