In this problem, we explore the effect on the standard deviation of adding the same constant to each data value in a data set. Consider 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.
Answers
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
Related Questions
dul Tunction is shown on the graph below.
A
What are the domain and range for the quadratic function shown on the graph?
A Range: All real numbers less than or equal to 7
B Range: All real numbers greater than or equal to 6 and less than or equal to 7
C Range: All real numbers
D Range: All real numbers less than 7
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Answer:
Step-by-step explanation:
A
What’s the function of f(x)=-2/3x -7 ?
Answers
Answer:
F(x) = -1/3 x^2 - 7x + C
please help !!! urgent ☹️
Answers
Answer:
20/8
=2.5
14×2.5=35
[tex] \frac{20}{8} = \frac{x}{14} \\ x = \frac{20 \times 14}{8} \\ x = \frac{280}{8} \\ x = 35[/tex]
Deshaun has scored 86, 83, 93, and 79 on her previous four tests. What score does he need on his next test so that his average (mean) is 86?
Answers
Answer:
89
Step-by-step explanation:
341 ( total of previous 4 tests) + 89= 430
Divide 430 by 5 ( number of tests)
if (-1,4) and (3,-2) are end points of diameter of the circle, then the equation of the circle is
Answers
Answer:
If you've more doubts you can ask :)
Step-by-step explanation:
If the centre of a circle is (a, b) and radius r, then the equation of the circle is :
[tex](x - x)^2 + (y-b)^2 = r^2[/tex]
First we will find the centre, (a , b):
[tex]a = \frac{3+(-1)}{2} = \frac{2}{2} = 1\\\\b = \frac{-2 + 4}{2} = \frac{2}{2} = 1[/tex]
Find radius:
[tex]Radius, r = \frac{Diameter}{2}[/tex]
Diameter is the distance between (-1, 4) and (3, -2)
[tex]diameter = \sqrt{(x_2 - x_1)^2 +(y_2-y_1)^2} \\\\[/tex]
[tex]= \sqrt{(3-(-1)^2 + (-2-4)^2} \\\\=\sqrt{16 + 36}\\\\=\sqrt{52}\\\\=\sqrt{4 \times 13}\\\\=2\sqrt{13} \ units[/tex]
Therefore , [tex]r = \frac{2 \times \sqrt{13} }{2} = \sqrt{13} \ units[/tex]
Equation of the circle is :
[tex](x - 1)^2 +(y-1)^2 = 13[/tex]
find the perfect square
-6x=3x^2+9
Answers
Answer:
[tex] - 6x = 3 {x}^{2} + 9 \\ 3 {x}^{2} + 6x + 9 = 0 \\ {x}^{2} + 2x + 3 = 0 \\ so \\ ether \: x = - 2 \\ or \: x = 1 [/tex]
how to set this up to solve
Answers
Answer:
use the arthmetic mean
Step-by-step explanation:
cos90degrees cos30 degrees + sec-squared45degrees sin30degrees - cos270degrees sin180degrees
Answers
Step-by-step explanation:
[tex]\cos 90 \cos 30 + \sec^2 45 \sin 30 - \cos 270 \sin 180[/tex]
But we know that
[tex]\cos 90 = \cos 270 = \sin 180 = 0[/tex]
and
[tex]\sin 30 = \dfrac{\sqrt{3}}{2} \:\:\text{and}\:\: \sec 45 = \sqrt{2}[/tex]
so this leaves us with just
[tex]\sec^2 45 \sin 30 = (\sqrt{2})^2 \left(\dfrac{\sqrt{3}}{2} \right)= \sqrt{3}[/tex]
A store manager can spend at most $1,000 a day for operating costs and payroll. It costs $100 each day to operate the store and $30 dollars a day for each employee. Use the following inequality to determine how many employees the manager can afford for the day, at MOST.
30x + 100 < 1000
A. X > 30
B. X > 33
C. X < 33
D. X < 30
Answers
Answer:
x < 30
Step-by-step explanation:
Given the inequality expression that denotes the statement as;
30x+100 < 1000
Subtract 100 from both sides
30x + 100 - 100 <1000 - 100
30x < 900
Divide both sides by 30
30x/30 < 900/30
x < 30
Hence the required solution is x < 30
The number of employee the manager can afford a day is x < 30.
The given parameters:
Amount spent a day for operating cost = $1,000The operating cost of the store, = $100 per dayAmount paid to the employee = $30 per dayThe inequality of the number of employee the manager can afford a day is calculated as follows;
30x + 100 < 1000
collect similar terms together;
30x < 1000 - 100
30x < 900
divide both sides of the equation by 30;
[tex]x <\frac{900}{30} \\\\x <30[/tex]
Thus, the number of employee the manager can afford a day is x < 30.
Learn more about solution to inequality here: https://brainly.com/question/24372553
please help this is due today! geometry
Find the distance between the points (4.3) and (0, 3).
Answers
Answer is 4 units
Explanation:
See the image as mathematical signs can’t be written here
Only answer if you're very good at Math.
Given f (x) = x + 1 and g(x) = x^2, what is
( g o f) (x)?
A: ( g o f) (x) = x^2 + 1
B: ( g o f) (x) = (x + 1)^2
C: ( g o f) (x) = x ^ 2 + x + 1
D: ( g o f) (x) = x^2 (x + 1)
Answers
Answer:
Solution given:
f(x) = x +1 and g(x) = x²,
now
(gºf)(x) =g(fx)=g(x+1)=(x+1)²
B) (gºf)(x) = (x + 1)^2
Find the surface area of the figure.
Answers
Answer:
The surface area of the figure is 452.2m2 (A)
The model below represents the sum of two mixed numbers.
Write an equation that shows the sum represented by the model.
Show your work.
Answers
Answer:
hey I am not sure about the answer but I guess this is the right answer:
(x+3)+x
Factor over the complex numbers, if possible: x² + 2xyi - y2
What is the answer?
Answers
9514 1404 393
Answer:
(x +yi)²
Step-by-step explanation:
Comparing the given expression to the square of a binomial, we can determine the given expression to be a square.
(a +b)² = a² +2ab +b²
Here, we have a=x and b=yi. Then the factorization is ...
x² +2xyi +(yi)² = (x +yi)²
The two given figures are similar. Which statements must be true? Select all that apply.
Answers
Answer:
angle B=74°
Step-by-step explanation:
the shapes are similar
Choose each number that shows 4% as an equivalent fraction, decimal, or percent. Select all that apply.
Answers
Answer:
1/4
Step-by-step explanation:
4 divide in half so should be 1/4
Let’s Say I Left The House At 11:32 And Then I Came Back At 1:42, How Many Hours Have I Been Gone.
Example: 1hours and 20min
Just an example not the answer ^
Answers
i think the correct answer is 2 hours and 10 mins
3. It refers to the number of values an interval may contain
a. class interval
c. frequency
b. class width
d. range
Answers
Answer:
An interval scale is one where there is order and the difference between two values is meaningful. Examples of interval variables include: temperature (Farenheit), temperature (Celcius), pH, SAT score (200-800), credit score (300-850).
Step-by-step explanation:
thank me later
Given: g(x) = x - 4 and h(x) = 2x - 8. What is g(h(1011?
Answers
Answer:
[tex]g(h(1011)) = 2010[/tex]
Step-by-step explanation:
Given
[tex]g(x) = x - 4[/tex]
[tex]h(x) =2x - 8[/tex]
Required
[tex]g(h(1011)[/tex]
First, we calculate [tex]g(h(x))[/tex]
[tex]g(x) = x - 4[/tex]
Substitute h(x) for x
[tex]g(h(x)) = h(x) -4[/tex]
Substitute [tex]h(x) =2x - 8[/tex]
[tex]g(h(x)) = 2x - 8 -4[/tex]
[tex]g(h(x)) = 2x -12[/tex]
Substitute 1011 for x
[tex]g(h(1011)) = 2*1011 -12[/tex]
[tex]g(h(1011)) = 2022 -12[/tex]
[tex]g(h(1011)) = 2010[/tex]
Answer:
6
Step-by-step explanation:
just did it on egde 2021
How do you find the square root of 11? I need to show work
Answers
Answer:3.31662479036.
Step-by-step explanation:To find the square root of 11, use the long division method to get the approximate value. Therefore, √11 = 3.31662479036. Register at BYJU'S to learn other interesting mathematical concepts.
The population of a town grows at a rate proportional to the population present at time t. The initial population of 500 increases by 10% in 10 years. What will be the population in 20 years? (Round your answer to the nearest person.)
510
Incorrect: Your answer is incorrect.
persons
How fast (in persons/yr) is the population growing at
t = 20?
(Round your answer to two decimal places.)
persons/yr
Answers
Answer:
The right answer is "605 persons".
Step-by-step explanation:
Given that,
⇒ [tex]\frac{dP}{dt} \alpha P[/tex]
or,
⇒ [tex]\frac{dP}{dt} =RP[/tex]
⇒ [tex]\frac{1}{R} \int\limits^{PT}_{500} {\frac{dP}{P} } = \int\limits^{t}_{0} dt[/tex]
⇒ [tex]\frac{1}{R} [log PT-log500]=t[/tex]
⇒ [tex]log[\frac{PT}{500} ]=Rt[/tex]
At t = 10 years,
⇒ [tex]PT=\frac{110}{100}\times 500[/tex]
[tex]=550[/tex]
∴ [tex]log[\frac{550}{500} ]=R\times 10[/tex]
[tex]R=\frac{log(1.1)}{10}[/tex]
At t = 20,
⇒ [tex]log{\frac{PT}{500} }=\frac{log \ 1.1}{10}\times 20[/tex]
[tex]PT=500\times (1.1)^2[/tex]
[tex]=605 \ persons[/tex]
PLEASE HELP!!!! WHOEVER GETS IT RIGHT GETS BRAINLIEST !!!!
FIND THE VALUE OF X
Answers
Answer:16 degree is the answer.
Since r and m are parallel:
10x-3=7x+45
3x=48
x=16
Here are Barry Bonds's home-run totals, mostly for the San Francisco Giants,
during the years 1991 - 2005:
25, 34, 46, 37, 33, 42, 40, 37, 34, 49, 73, 46, 45, 45, 5
There are two outliers at opposite ends of this distribution: his 5 home runs in
2005 and his 73 home runs in 2001. Which of the following is a modified box
plot for this distribution?
A.
B.
C..
E.
Answers
The modified boxplot created for the distribution is boxplot E
Given the values :
25, 34, 46, 37, 33, 42, 40, 37, 34, 49, 73, 46, 45, 45, 5
The outliers in the values are : 5 and 73
Hence, the modified values are :
25, 34, 46, 37, 33, 42, 40, 37, 34, 49 , 46, 45, 45
Using a boxplot maker or excel, we could use the modified data to create a boxplot with the following properties as obtained from the boxplot shown below :
Median value = 40
Minimum = 25
Maximum = 49
First quartile = 34
Third quartile = 45.5
The modified boxplot has no outlier and it corresponds with the boxplot in option E
Learn more : https://brainly.com/question/1523909
Answer:
graph C
Step-by-step explanation:
What is length of DF?
Answers
Answer:
DF = 11
Step-by-step explanation:
From the question given above, the following data were obtained:
EH = 8
HG = 3
EF = DG
DF =?
Since, EF = DG, it also means that EG = DF.
Next we shall determine EG. This can be obtained as follow:
EG = EH + HG
EH = 8
HG = 3
EG = 8 + 3
EG = 11
Finally, we shall determine EF. This is illustrated below:
EG = DF
EG = 11
DF =?
11 = DF
Therefore,
DF = 11
I need help with this problem
Answers
Answer:
x = 9 , jk = 42 , kl= 78
Step-by-step explanation:
Explained in the paper.
Goodluck
Answer:
x = 9
Step-by-step explanation:
[tex](4x+6)+(7x+15)=120[/tex]
[tex](4(9)+6)+(7(9)+15)=120[/tex]
[tex](36+6) + (63+15)=120[/tex]
[tex](42)+(78)=120[/tex]
x = 9
JL = 42
KL = 78
Simplify − { − ( + ) − ÷ }
Answers
Answer:
- (- (+) - ÷ )
+) (-) (+) (-)
= (+) (-)
Select all the possible names for the following angle
Answers
Answer:
The answers are options d and e
See the image for question :)
Answers
Answer:
it is simple just compare the ratios simple as that
but I will need to know all the formula s
it says 10^-4
please help give brainliest
Answers
Answer:
jane is correct
Step-by-step explanation:
10⁻⁴ can be written as [tex]\frac{1}{10000}[/tex] and as 0.0001
The distance from Nairobi, Kenya to Pretoria, South Africa is 3,969 kilometers. The distance from Cairo, Egypt to Tunis, Tunisia is 2,811 kilometers. Estimate the difference between these two distances by first rounding to the nearest hundred. i need help pleasee
Answers
Answer:
Step-by-step explanation:
3,969 = 4,000 rounded to nearest hundred
2,811=3,000 rounded to nearest hundred
therefore... the difference is 4,000 - 3,000 = 1,000 kilometers
Answer:1,100
Step-by-step explanation:
rounding 3,969 to the nearest hundreds is 4,000 and rounding 2811 to the nearest hundred is 2900. Now you subtract 4000-2900 = 1100.