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Brrunno [24]
3 years ago
6

In this problem, we explore the effect on the standard deviation of adding the same constant to each data value in a data set. C

onsider the following data set.
8, 16, 14, 8, 16

(a) Use the defining formula, the computation formula, or a calculator to compute s. (Enter your answer to four decimal places.)

(b) Add 8 to each data value to get the new data set 16, 24, 22, 16, 24. Compute s. (Enter your answer to four decimal places.)

(c) Compare the results of parts (a) and (b). In general, how do you think the standard deviation of a data set changes if the same constant is added to each data value?

Adding the same constant c to each data value results in the standard deviation remaining the same.

Adding the same constant c to each data value results in the standard deviation increasing by c units.

Adding the same constant c to each data value results in the standard deviation decreasing by c units.

There is no distinct pattern when the same constant is added to each data value in a set.

Mathematics
1 answer:
aliya0001 [1]3 years ago
6 0

Answer:

3.6661

3.6661

A, Adding a constant does nothing to the standard deviation

Step-by-step explanation:

I'm gonna assume s=standard deviation

The standard deviation is just the square root of the second moment minus the first moment squared

Because we were not told otherwise I think it's pretty safe to assume that all events are equally likely

Let's start by calculating the first moment (AKA The mean)

1/5(8+16+14+8+16)= 12.4

Let's then find the second moment

1/5(8²+16²+14²+8²+16²)= 167.2

√(167.2-12.4²)=3.6661

b.

While I could just tell you that adding something to the standard deviation (and the variane as well) doesn't do anything let's calculate it for fun

same process

.2(16+24+22+16+24)= 20.4

.2(16²+24²+22²+16²+24²)=429.6

√(429.6-20.4²)= 3.6661

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Determine which of the four levels of measurement​ (nominal, ordinal,​ interval, ratio) is most appropriate. ages of children: 3
gayaneshka [121]

Answer:

The level of variable ages of children is ratio.

Explanation:

Nominal scale is the one which takes categories as its values like gender of a person.

Ordinal scale is the one which is used to show the order of values with no clear difference among them like satisfaction level of people with a service.

Interval scale is the one which shows the clear order of values with clear difference between the values with out true zero.

Ordered scale is one which not only produces the order of variables but also makes the difference between variables known along with information on the value of true zero.

Therefore, the variable which is under consideration here is the ages of children, which takes the values 3,4,5,6 and 7 is a ratio scale.


6 0
3 years ago
Let f(x)= 100 / −10+ e^ −0.1x . What is f(−6) ?
bija089 [108]

The value of f(-6) is -12.2

Explanation:

Given that the function f(x)=\frac{100}{-10+e^{-0.1\left(x\right)}}

We need to determine the value of f(-6)

The value of f(-6) can be determined by substituting the value for x=-6 in the function and simplify the function.

Hence, let us substitute x=-6 in the function, we get,

f(-6)=\frac{100}{-10+e^{-0.1\left(-6\right)}}

Let us apply the rule -\left(-a\right)=a , we get,

f(-6)=\frac{100}{-10+e^{0.1\left(6\right)}}

Multiplying the numbers, we get,

f(-6)=\frac{100}{-10+e^{0.6}}

The value of e^{0.6}=1.822

Substituting the value of e^{0.6}=1.822 , we get,

f(-6)=\frac{100}{-10+1.822}

Subtracting the denominator, we have,

f(-6)=\frac{100}{-8.178}

Dividing, we have,

f(-6)=-12.228

Rounding off to the nearest tenth, we have,

f(-6)=-12.2

Thus, the value of f(-6) is -12.2

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