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Oksana_A [137]
2 years ago
5

A. Create a set of 5 points that are very close together and record the standard deviation. Next, add a sixth point that is far

away from the original 5 and record the new standard deviation. What is the impact of the new point on the standard deviation?
Mathematics
1 answer:
defon2 years ago
7 0

Answer: The addition of the new point alters the previous standard deviation greatly

Step-by-step explanation:

Let the initial five points be : 2 3 4 5 and 6. In order to calculate the standard deviation for this data, we will need to calculate the mean first.

Mean = summation of scores/number of scores.

The mean is therefore: (2+3+4+5+6)/5 = 20/5 = 4.

We'll also need the sum of the squares of the deviations of the mean from all the scores.

Since mean = 4, deviation of the mean from the score "2" = score(2) - mean (4)

For score 3, it is -1

For 4, it's 0

For 5 it's 1

For 6 it's 2.

The squares for -2, -1, 0, 1, and 2 respectively will be 4, 1 , 0, 1, 4. Summing them up we have 10 i.e (4+1+0+1+4=10).

Calculating the standard deviation, we apply the formula:

√(summation of (x - deviation of mean)^2)/N

Where N means the number of scores.

The standard deviation = √(10/5) = 1.4142

If we add another score or point that is far away from the original points, say 40, what happens to the standard deviation. Let's calculate to find out.

i.e we now have scores: 2, 3, 4, 5, 6 and 40

We calculate by undergoing same steps.

Firstly mean. The new mean = (2+3+4+5+6+40)/6 = 60/6 = 10.

The mean deviations for the scores : 2, 3, 4, 5, 6 and 40 are -8, -7, -6, -5, -4 and 30 respectively. The squares of these deviations are also 64, 49, 36, 25, 16 and 900 respectively as well. Their sum will then be 1090. i.e. (64+49+36+25+16+900 = 1090).

The new standard deviation is then=

√(1090/6)

= √181.67

= 13.478.

It's clear that the addition of a point that's far away from the original points greatly alters the size of the standard deviation as seen /witnessed in this particular instance where the standard deviation rises from 1.412 to 13.478

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Anton [14]

Answer: Y= -3/4x+13


Step-by-step explanation:

A line passes through the point (8,7) and has a slope of negative 3/4 Write an equation in slope-intercept form for this line.

This is what i get

Slope of a line Y= mx+b

Y= 7

X= 8

M= -3/4


7= -3/4(8)+b

7= -6+b

7+6=b

13=b


Y= -3/4x+13

6 0
3 years ago
Find m angle TUV if m angle TUN=1+38 pi m angle NUV=66^ m angle TUV=105x
ipn [44]

Answer:

m∠TUV = 105

Step-by-step explanation:

From the question given above, the following data were obtained:

m∠TUN = 1 + 38x

m∠NUV = 66°

m∠TUV = 105x

m∠TUV =?

Next, we shall determine the value of x. This can be obtained as illustrated below:

m∠TUV = m∠TUN + m∠NUV

105x = (1 + 38x) + 66

105x = 1 + 38x + 66

Collect like terms

105x – 38x = 1 + 66

67x = 67

Divide both side by 67

x = 67 / 67

x = 1

Finally, we shall determine the value of m∠TUV. This can be obtained as shown below:

m∠TUV = 105x

x = 1

m∠TUV = 105(1)

m∠TUV = 105

5 0
3 years ago
Please help! what is y+7=-1/7(x+4) in slope intercept form?
Stells [14]
We know that
the equation of a line in <span>slope intercept form is--------------> y=mx+b
where
m-----------> is the slope
b-----------> is the y-intercept  point when x=0

</span><span>y+7=-1/7(x+4)---------> y+7=(-1/7)x-4/7
</span>y+7=(-1/7)x-4/7------> y=(-1/7)x-4/7-7------> y=(-1/7)x-(53/7)

the answer is
y=(-1/7)x-(53/7)-------------> this is the equation of a line in slope intercept form
m=(-1/7)=-0.14
b=(-53/7)=-7.57
y=-0.14x-7.57

see the attached figure

6 0
2 years ago
Using exponent laws please answer this
hram777 [196]

Answer:

  see below

Step-by-step explanation:

In addition to the exponent rule ...

  (a^b)^c = a^(bc)

it is helpful to know the first few powers of some small integers.

  5^3 = 125

  9^2 = 81

  4^3 = 64

  2^6 = 64

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  1. 125^3 = (5^3)^3 = 5^(3·3) = 5^9
  2. 81^7 = (9^2)^7 = 9^(2·7) = 9^14
  3. (1/64)^3 = ((1/4)^3)^3 = (1/4)^(3·3) = (1/4)^9
  4. (1/64)^3 = ((1/2)^6)^3 = (1/2)^(6·3) = (1/2)^18
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Number sense write a six-digit number in which the digit 4 has the value of 40,000
topjm [15]

You just need to add any digit in front of 40,000 for a 6-digit number meeting those requirements.

Hope this helps!

4 0
2 years ago
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