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a_sh-v [17]
2 years ago
7

Four integers have a mean of 12, a median of 14, a mode of 14 and a range of 12.

Mathematics
1 answer:
Zina [86]2 years ago
5 0

Answer:

4, 14, 14, 16

Step-by-step explanation:

<u>Key</u><u> </u><u>skills</u><u> </u><u>needed</u><u>:</u><u> </u><u>Casework</u><u>,</u><u> </u><u>Mean</u><u>,</u><u> </u><u>Median</u><u>,</u><u> </u><u>and</u><u> </u><u>Mode</u>

1) We start with 4 numbers _ _ _ _

2) We can determine two of the numbers by using the fact that the median is 14 and the mode is 14.

3) The numbers would have to be:

  • _ 14 14 _
  • _ 14 14 14

The 2nd one does not work because the last number would have to be a 6 to have a mean of 12, but the range would not be 12.

4) So, our numbers are _ 14 14 _

5) The two numbers add up to 20 (in order to have a mean of 12. If you subtract the bigger one by the smaller one, it will be 12.

6) We can make a system: saying x is the bigger number and y is the smaller number.

x + y = 20

x - y = 12

Add both and you will get 2x = 32 (since the y values cancel out).

7) divide by on both sides, and x = 16.

8) To find y, we can plug x back in to one equation:

16 + y = 20

y = 4

Our smaller number is 4 and our bigger number is 16.

9) Therefore the numbers are: 4, 14, 14, 16

<em>Hope</em><em> </em><em>you</em><em> </em><em>understood</em><em> </em><em>and</em><em> </em><em>have</em><em> </em><em>a</em><em> </em><em>nice</em><em> </em><em>day</em><em>!</em><em>!</em><em> </em><em>:</em><em>D</em>

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