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ycow [4]
3 years ago
15

Here are 10 test scores: 50, 74, 76, 77, 78, 79, 80, 80, 82, 84. The mean of these scores is 76. How does removing the outlier 5

0 affect the mean?
A.
The set has 50 as an outlier and removing it decreases the mean by about 6.

B.
The set has 50 as an outlier and removing it decreases the mean by about 2.

C.
The set has 50 as an outlier and removing it increases the mean by about 3.
Mathematics
1 answer:
vitfil [10]3 years ago
8 0
The answer is C. 
<span>The set has 50 as an outlier and removing it increases the mean by about 3.

Since 50 is significantly smaller number than all others, it is expected that removing 50 will increase the mean.
The first mean is 76:
</span>X_{1} = \frac{50+74+76+77+78+79+80+80+82+84}{10} =  \frac{760}{10} =76
<span>
The mean after removing 50 is:
</span>X_{2} = \frac{74+76+77+78+79+80+80+82+84}{10} = \frac{710}{90} =78.89
X₂ ≈ 79<span>
</span>
The difference between the second and the first mean is 79 - 76 = 3, thus 
<span>removing 50 as an outlier increases the mean by about 3.</span>
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length of the pool = length of the yard * 1/2

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By replacing the 60 m for the length of the yard and 50 m for the width, we get:

length of the pool = 60 * 1/2 = 30

width of the pool = 50 * 1/2 = 25

Let's call x1 to the distance from the base of the pool to the bottom side of the yard and x2 to the distance from the top side of the pool to the top side of the yard, then we can formulate the following equation:

width of the yard = width of the pool + x1 + x2

Since we want the edges to be at an equal distance, x1 and x2 are the same, then we can rewrite them as x:

width of the yard = width of the pool + x + x

width of the yard = width of the pool + 2x

Replacing the known values:

60 = 30 + 2x

From this equation, we can solve for x to get:

60 - 30 = 30 - 30 + 2x

30 = 2x

30/2 = 2x/2

15 = x

x = 15

Now, let's call y1 to the distance from the right side of the corresponding side of the yard and y2 to the distance from the left side of the pool to the left side of the yard, with this, we can formulate the following equation:

length of the yard = length of the pool + y1 + y2

Since we want the edges to be at an equal distance, y1 and y2 are the same, then we can rewrite them as y:

length of the yard = length of the pool + y + y

length of the yard = length of the pool + 2y

Replacing the known values:

50 = 25 + 2y

50 - 25 = 25 - 25 + 2y

25 = 2y

25/2 = 2y/2

12.5 = y

y = 12.5

Now, we know that the pool must be at a distance of 15 m from the horizontal sides of the pool to the horizontal sides of the yard and that it must be at a distance of 12.5 m from the vertical sides of the pool to the vertical sides of the yards.

Here is a figure that depicts the results:

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Answer:

1.

x = 44*2

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2.

x = 62*2

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x = 160/2

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6.

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