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inna [77]
3 years ago
8

What is the mean and mad of this data set?

Mathematics
1 answer:
larisa86 [58]3 years ago
5 0

Answer:

The mean number of gerbils seen per day is 6.

The mean absolute deviation of the data is 2.29.

Step-by-step explanation:

The mean of a data set is the value that represents the entire data set. It is the average value.

The formula to compute the mean of a data set is:

\bar x=\frac{1}{n}\sum X

The mean absolute deviation (MAD) of a data set is the average distance amid each value and the mean. The MAD provides us with an idea about the deviation in the data set.

The formula to calculate the value of MAD is:

MAD=\frac{1}{n}\sum |x-\bar x|

The data set for the number of gerbils seen per day is:

S = {2, 3, 5, 7, 8, 8, 9}

Compute the mean of the data as follows:

\bar x=\frac{1}{n}\sum X

  =\frac{1}{7}\times [2+3+5+7+8+8+9]\\\\=\frac{1}{7}\times 42\\\\=6

The mean number of gerbils seen per day is 6.

Compute the mean absolute deviation of the data as follows:

MAD=\frac{1}{n}\sum |x-\bar x|

          =\frac{1}{7}\times [|2-6|+|3-6|+|5-6|+|7-6|+|8-6|+|8-6|+|9-6|]\\\\=\frac{1}{7}\times 16\\\\=2.2857\\\\\approx 2.29

Thus, the mean absolute deviation of the data is 2.29.

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In a triangle, the sum of the measures of the first two angles is 12 less than the measure of the third angle. In addition, the
PSYCHO15rus [73]

the sum of the internal angles of a triangle are equal to 180 degrees.

once i remembered that the problem became a lot easier.

let a, b, and c be the angles of the triangle.

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let a = 2*b

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let c = a+b-12

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the above two statements are given.

since the sum of the internal angles of a triangle are equal to 180, then we have a third equation to work with which is

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a + b + c = 180

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we now have 3 equations for 3 unknowns and we should be able to solve for each of the unknowns.

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it looks like the easiest thing is to solve for b. once we find b, the rest should fall into place very nicely.

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since a = 2*b, we can substitute 2*b for a in the equation a + b + c = 180.

that equation then becomes 2*b + b + c = 180 which becomes 3*b + c = 180.

looking at the equation c = a + b - 12, we solve for b as follows:

since we know that a = 2 * b, we can substitute 2*b for a and the equation becomes c = 2*b + b - 12 which becomes c = 3*b - 12.

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the equation we are working with is 3*b + c = 180 which originally started as a + b + c = 180.

we can substitute 3*b - 12 for c and the equation becomes

3*b + 3*b - 12 = 180 which becomes 6*b = 192 after adding 12 to both sides and combining like terms.

dividing both sides of the equation by 6 and we get b = 32 degrees.

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we have b = 32 degrees.

we have a = 2 * b so a = 64 degrees.

we have c = a + b - 12 which becomes c = 32 + 64 - 12 which becomes c = 96 - 12 which becomes c = 84 degrees.

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substituting in the equation a + b + c = 180, we get 32 + 64 + 84 = 180 which becomes 96 + 84 = 180 which becomes 180 = 180.

-----

answer is:

a

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Answer:

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