Critical Thinking: Data Transformation In this problem, we explore the effect on the standard deviation of multiplying each data value in a data set by the same constant. Consider the data set 5, 9, 10, 11, 15.
(a) Use the defining formula, the computation formula, or a calculator to compute s.
(b) Multiply each data value by 5 to obtain the new data set 25, 45, 50, 55, 75. Compute s.
(c) Compare the results of parts (a) and (b). In general, how does the standard deviation change if each data value is multiplied by a constant c?
(d) You recorded the weekly distances you bicycled in miles and computed the standard deviation to be s 3.1 miles. Your friend wants to know the standard deviation in kilometers. Do you need to redo all the calcula- tions? Given 1 mile 1.6 kilometers, what is the standard deviation in kilometers?

Answers

Answer 1

Answer:

Kindly check explanation

Step-by-step explanation:

Given the data : 5, 9, 10, 11, 15

s = √[(ΣX - m)² / (n - 1)]

n = number of sample = 5

m = mean

m = ΣX/n

m = (5 + 9 + 10+ 11 + 15) / 5

m = 50/5 = 10

s =√((5-10)^2 + (9-10)^2 + (10-10)^2 + (11-10)^2 + (15-10)^2) / 5-1

= 3.601

(B) Multiply each data value by 5 to obtain the new data set 25, 45, 50, 55, 75. Compute s.

m = ΣX/n

m = (25 + 45 + 50 + 55 + 75) / 5

m = 250/5 = 50

s =√((25-50)^2 + (45-50)^2 + (50-50)^2 + (55-50)^2 + (75-50)^2) / 5-1

= 18. 028

(c) Compare the results of parts (a) and (b). In general, how does the standard deviation change if each data value is multiplied by a constant c?

The standard deviation changes by almost c times multiplied by the initial value.

3.601 * 5 = 18.005 which is almost equivalent to 18.028

(d) You recorded the weekly distances you bicycled in miles and computed the standard deviation to be s 3.1 miles. Your friend wants to know the standard deviation in kilometers. Do you need to redo all the calcula- tions?

No

Given 1 mile 1.6 kilometers, what is the standard deviation in kilometers?

If 1 mile = 1.6km

s = 3.1 miles

s in kilometers = (1.6 * 3.1) = 4.96km


Related Questions

Activity
Blaine is selling tickets to a rock concert. Tickets in the front section cost $60 each. Tickets in the back section cost $40
each. Blaine has 55 tickets left to sell, and to meet his sales quota he needs to sell more than $600 in tickets from the
remaining tickets.
Blaine makes a profit of $40 on every ticket for the front section. He makes a profit of $25 on every ticket for the back
section. What's the maximum profit Blaine can make from selling his remaining tickets?
You may find it helpful to review the steps of linear programming e.
Part A
Write the system of inequalities for the given situation where x represents the number of front section tickets and y
represents the number of back section tickets.

Answers

Answer:

25 tickets more

Step-by-step explanation:

I got x+y is (less than or equal to) 55 for the first inequality and 60x+40y>600 for the second one!

Step-by-step explanation:

Since Blaine can sell a maximum of 55 tickets, the first inequalitly is x+y is less than OR EQUAL TO 55. Since the tickets in the back section cost $40 each, 40y represents the money made from those tickets. Blaine needs to make 600 in sale so the inequality is 60x+40y>600.

Robert builds a rectangular deck with a length that is four less than two times the width of the deck.

Write the equation for the area of the deck, where w is the width.

Answers

Let

Width be wLength=2w-4

Now

[tex]\\ \sf\longmapsto Area=Length\times Breadth [/tex]

[tex]\\ \sf\longmapsto Area=w(2w-4)[/tex]

[tex]\\ \sf\longmapsto Area=2w^2-4w[/tex]

Is the point (-4, 5) a solution of the standard form equation -2x-2y=-2

Answers

Answer:

not that i know of

Step-by-step explanation:

Which relationships describe angles 1 and 2?
Select each correct answer.

complementary angles
adjacent angles
supplementary angles
vertical angles

Answers

Answer:

supplementary angles because they add 180 degrees

Step-by-step explanation:

hope this helped

Answer: Supplemetary Angels,  Adjacent Angels

B,C

Step-by-step explanation: The other person is wrong

sin
[tex] \sin( \binom{ - 11\pi}{3} ) \times \tan( \frac{35\pi}{6} ) \times \sec( - ) [/tex]

Answers

Answer:

solve it :)

Step-by-step explanation:

someone pliz solved = (27) -1/3×(27) -1/3×[(27) 1/3-(27) 2/3]​

Answers

ghjbgdg hgyi uhb hfik hidey jjtssg igsryi

Given that a=4 and b=5. evaluate : a²+3b​

Answers

Answer:

4² + 3(5)

= 4 × 4 + 15

= 16 + 15

= 31

Is it possible to have a triangle with the following sides give reason
3cm 4cm 5cm
4cm 5cm 6cm​

Answers

Answer: Yes,

Step-by-step explanation:

Because since there are two numbers that are the same and numbers that are different, you can make a triangle out of it. Since a triangle has twi sides that have the same length and a side that has a different length.

Example: 4cm 4cm

Which of the following is a correct statement about the number and the set it belongs to?

+ π is REAL and RATIONAL only.

+ None of these

+ Repeating decimals are REAL and IRRATIONAL.

+ 2515 is REAL and RATIONAL.

+ −25  is REAL, RATIONAL, INTEGER, WHOLE and NATURAL.​

Answers

9514 1404 393

Answer:

  2515 is REAL and RATIONAL

Step-by-step explanation:

π is irrational

Repeating decimals are rational.

-25 is neither a Whole nor Natural number. (Whole numbers are non-negative integers; Natural numbers are positive integers, sometimes including 0.)

Any integer or fraction is REAL and RATIONAL. 2515 is an integer, so it is ...

  2515 is REAL and RATIONAL

The y-intercept of the line whose equation is 5+y=2x

Answers

Answer:

(0, -5)

Step-by-step explanation:

We need to isolate y.

5+y=2x -- Subtract 5 from 5+y

y = 2x - 5

The image connected is what the graph would look like.

Answer:

y-int = (0,-5)

Step-by-step explanation:

Substitute 0 for x and solve to find the y-intercept.

[tex]5+y=2(0)\\ 5+y=0\\y=0-5\\y=-5[/tex]

Mathematics pls help 4 questions will give brain to best answer

Answers

Answer:

There probably isn't a mode.

Step-by-step explanation:

Because the numbers in this set of data are continuous, it is impossible to have a mode, the number that occurs most frequently in a set of data.

Answer:

[1] Not enough information to draw valid conclusion

[2] The mean will be 12.

[3] 14

[4] 5 and 7

Step-by-step explanation:

[1] if the range for a set of data is 24, from 2 to 26 and the mean is 17, what can you conclude about the data

17 is the typical data value.

Not enough information to draw valid conclusion.

The median will be 17 also.

There probably isn't a mode.

Answer: Not enough information to draw valid conclusion.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

[2] The extreme values in a set of data are 5 and 19. What is true about the data set?

The mean will be 12.

There is not enough data.

The range is 14.

There will be more than one mode.

Answer = The mean will be 12.

Explanation : Mean = add all values and divide by the number of values. 5+19=24, 24/2=12

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

[3] What is the mean for the following set of data, to the nearest whole number?

5,9,15,18,22

Answer = 14

Explanation:

5 + 9 + 15 + 18 + 22 = 69

69 / 5 = 13.8

Round 13.8 = 14

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

[4]  What is the mode for the following set of data?

4,5,5,6,7,7,8,12.

Mode = Most Often Seen

Answer = 5 and 7

Explanation:

Base on given you can see that the most is two number. There is two five and there is two seven.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

~Lenvy~

Evaluate the following expression:


Answers

Answer:

5.25

Step-by-step explanation:

The same sequence may be defined in three ways: 1) f(x) = 3x + 4 for x = {1, 2, 3, ...}, 2) a1 = 4 and an + 1 = an + 3 for n = {1, 2, 3, ...} and 3) an = 4 + 3(n − 1) for n = {1, 2, 3, ...}.
They are all supposed to generate the same values, but one version may contain an error. If one version contains an error, identify the one with the error and fix it.

Answers

Answer:

its B

Step-by-step explanation:

Help help math math ASAP

Answers

The answer is X is 4 y is -6. I can’t type the work, but this took a few minutes

find the value of 5 (x - 7) = 7x -5(pls answer)

Answers

Step-by-step explanation:

1,3x+9=44-2x3x+2x=44-95x=35 5=72.3x+6=x+23x-x=2-62x=-4 2x=2

BTW I'M SORRY IF THAT'S WRONG

Answer:

x = -15

Step-by-step explanation:

5 (x - 7) = 7x - 5

Remove the parentheses

5x - 35 = 7x - 5

Move the terms

5x - 7x = -5 + 35

Collect like terms Calculate

-2x = 30

Divide both sides

x = -15

PLEASE MARK ME AS BRAINLIEST AND HAVE A NICE DAY :)

5.16 Identify hypotheses, Part II: Write the null and alternative hypotheses in words and then symbols for each of the following situations. (a) Since 2008, chain restaurants in California have been required to display calorie counts of each menu item. Prior to menus displaying calorie counts, the average calorie intake of diners at a restaurant was 1100 calories. After calorie counts started to be displayed on menus, a nutritionist collected data on the number of calories consumed at this restaurant from a random sample of diners. Do these data provide convincing evidence of a difference in the average calorie intake of a diners at this restaurant?

Answers

Answer:

H₀: µ = 1100 vs. Hₐ: µ ≠ 1100.

Step-by-step explanation:

A null hypothesis is a sort of hypothesis used in statistics that intends that no statistical significance exists in a set of given observations.  

It is a hypothesis of no difference.

It is typically the hypothesis a scientist or experimenter will attempt to refute or discard. It is denoted by H₀.

For instance, H₀: µ = µ₀, where µ₀ is some null value or some claimed value.

Whereas, the alternate hypothesis is the contradicting statement to the null hypothesis.

The alternate hypothesis describes direction of the hypothesis test, i.e. if the test is left tailed, right tailed or two tailed.

It is also known as the research hypothesis and is denoted by Hₐ.

In this case the hypothesis can be defined as follows:

Null hypothesis:

H₀: The average calorie intake of a diner at this restaurant is 1100, i.e. µ = 1100.

Alternate hypothesis:

Hₐ: The average calorie intake of a diner at this restaurant is different from 1100, i.e. µ ≠ 1100.

Using the formula below or Excel, find the correlation coefficient, r, for this set of scores. Answer choices are rounded to the nearest hundredth.
r equals fraction numerator 1 over denominator n minus 1 end fraction sum from blank to blank of open parentheses fraction numerator x minus x with bar on top over denominator s subscript x end fraction close parentheses open parentheses fraction numerator y minus y with bar on top over denominator s subscript y end fraction close parentheses

Answers

The correlation coefficient measures the relationship between the two variables

The correlation coefficient is 0.234

How to determine the correlation coefficient

The formula of correlation coefficient is:

[tex]r = \frac{1}{n - 1} * \sum{(\frac{x - \bar x}{\sigma_x})*(\frac{y - \bar y}{\sigma_y})[/tex]

Using the dataset from the complete question, we have:

[tex]r = \frac{1}{5 - 1} * 0.9375[/tex]

Evaluate the difference

[tex]r = \frac{1}{4} * 0.9375[/tex]

Evaluate the quotient

[tex]r = 0.234375[/tex]

Approximate

[tex]r = 0.234[/tex]

Hence, the correlation coefficient is 0.234

Read more about correlation coefficient at:

https://brainly.com/question/4219149

A class has 36 students in it and 25% of the students wore hats to school.What fraction of the students wore hats?

Answers

Answer:

9/36 or 1/4

Step-by-step explanation:

Find the zeros of the function.
f(x) = 2x2 – 36

Answers

Answer:

3√2 and -3√2

Step-by-step explanation:

2x^2-36

2(x^2-36)

2(x+3√2)(x-3√2)

Answer:

-4.24 and 4.24

Step-by-step explanation:

If 2 L of water is mixed with 4.5 L of milk and filled into 650 mL cans. Then
cans will be needed to fill the mixture.

Answers

The numbers of can required to fill the mixture is 10 cans

Data;

Volume of water = 2Lvolume of milk = 4.5Lvolume of cans = 650mL = 0.65L

Number of Cans Required to fill the mixture

To find the numbers of can required to fill the mixture, let's add the volume of the mixture.

volume of mixture = volume of water + volume of milk

volume of mixture = [tex]2 + 4.5 = 6.5L[/tex]

The entire volume of the mixture is 6.5L.

To find the numbers of cans that'll fill the mixture, let us divide 6.5 by 0.65.

Number of can required = [tex]\frac{6.5}{0.65} = 10[/tex]

From the calculation above, we would need 10 cans to fill the mixture.

Learn more on division and proportions here;

https://brainly.com/question/870035

6. What is the area of OW?
(А) Зл
В) бл

D) 36л

Answers

Answer:

B

Step-by-step explanation:

PLS HELP AGIAN if u guess just for points ill report you question in the picture

Answers

Answer:

[tex]\sf y = \dfrac{17}{2}[/tex]

explanation:

[tex]\sf 7y-4=9y+13-4y[/tex]

collect variables in one side

[tex]\sf 7y -9y +4y = 13 +4[/tex]

simplify by addition and subtraction

[tex]\sf 2y = 17[/tex]

divide both sides by 2

Hence, ,final answer:

[tex]\sf y = \dfrac{17}{2}[/tex]

Answer:

A.   y = 17/2

Step-by-step explanation:

Given equation:

7y - 4 = 9y + 13 - 4y

Collect like terms:

7y - 4 = 9y - 4y + 13

Combine like terms:

7y - 4 = 5y + 13

Subtract 5y from both sides:

2y - 4 = 13

Add 4 to both sides:

2y = 17

Divide both sides by 2:

y = 17/2

Find the LCM of 4 and 42

Answers

Answer:

84

Step-by-step explanation:

How many whale sharks would a researcher need to measure so that 90% confidence level would have a margin of error of 0.25

Answers

About 1407 sharks would be needed to have a margin of error of 0.25

What is margin of error?

Margin of error is used to determine by what value there is deviation from the real value. Margin of error (E) is given by:

[tex]E=Z_\frac{\alpha}{2} *\frac{standard\ deviation}{\sqrt{sample\ size} }[/tex]

The 90% confidence level have a z score of 1.645. Hence for E = 0.25, standard deviation = 5.7 feet, hence:

[tex]0.25=1.645*\frac{5.7}{\sqrt{sample\ size}}\\ \\sample\ size=1407[/tex]

About 1407 sharks would be needed to have a margin of error of 0.25

Find out more on margin of error at: https://brainly.com/question/10218601

Answer questions for points

Answers

Step-by-step explanation:

wat questions are we needed to answer

Answer:

Hello! Thank you for the points! Trying to rank up here!

$140.00 for 17ft squared

Answers

Answer: what is the question tho???

We can’t see the question...

Morgan needs 3 gallons of paint to paint the walls in his bedroom.
If the paint he uses costs $24 per gallon, how much will he spend
on paint to paint his room?
A. $24
B. $ 48
C. $60
D. $72
7.RP.A.1

Answers

Answer:

72

Step-by-step explanation:

You multiply 3 by 24 to get 72

She well need 72$ 24 x 3 is 72

The system has no solution.
The system has a unique solution:
System B
(x, y)= (1
x+4y=4
-x=4y-4
O The system has infinitely many solutions.
They must satisfy the following equation:
y= 0

Answers

Answer:

21

Step-by-step explanation:

Just add then multiplay the numbers.

help with all of these please ! i’m on a time limit and i don’t have much time left.

Answers

Answer:

1.  10.235

2.  213.5

3.  46

4.  225

5.  530

besties i need help !!
please help asap

Answers

Answer:

the answer is 623.1.

Step-by-step explanation:

The way this question should be written to be correct scientific notation is 2.3x10^5 + 3.6x10^6 which would equal 3.83x10^6

Other Questions
In a full paragraph (4-5 sentences), list what major historical event this political cartoon is referring to and explain what argument the artist is making. A skydiver has a mass of 80 kg. When she is at a height of 900 m, her GPE is705,600 J. She is falling at a velocity of 32 m/s downward. What is her ME at thispoint? There are 4 adults chaperones for every 15 students who attend a school field trip. If there are 135 students, how many adults would be there on the field trip. The ratio of gold beads to black beads on a Mizzou necklace is 2:3. If the necklace has 28 gold beads, how many black beads does it have? During mitosis, a single cell divides to produce two daughter cells. Whatmust happen in the original cell so that each of the daughter cells has acompiate set of chromosomes? Who are they?(Create adefinition forthem based onTHIS PERIODOF TIME)Adolf hitler Ken is making trail mix for his next hiking club meeting. He mixes 2 pounds of peanuts, 2pounds of raisins, and 1 pound of chocolate chips. His little sister begs him for a snack, so hegives her 5 ounces of the trail mix. Then, he portions out the rest for his meeting. If Kensplits the remaining trail mix evenly among 25 snack bags, how many ounces of trail mix willeach bag have?ounces PARAGRAPH ESSAY PROPAGANDA describe why propaganda is used by governments on their people ( I will give u 50 points) Fill in the blank below:Yoa Puerto RicoA. viajB. viajaronC. viaje Which sectional tension was the result of Henry Clay's American System?The North was opposed to the National Road.The South was opposed to states' rights.The North was opposed to the National Bank.The South was opposed to the tariffs. What other groups besides the Ku Klux Klan worked to reduce support forRepublicans in the South?A. The Whites Against Republicans and the White Democrats forPowerB. The White League and the Knights of the White CamelliaC. The Government of Purity League and the Knights in White SatinD. The NAACP and the Negro College Fund 15. Mr. Ryan at Ryan's Sporting Goods planto order 1344 baseballs. Baseballs arepackaged in cartons that each contain24 baseballs. How many cartons shouldMr. Ryan order?A 60 RABG 56CO 54DO 51 R20 Your family has decided to put a rectangle patio in your backyard similar to the shape of your backyard. Your backyard has a length of 40 feet and a width of 20 ft the length of your patio is 12 feet. Find the perimeter of your new patio. Answer this question in three to four sentences.How can a participant in a group discussion be an effective speaker? John adams passed the ___ act to punish anyone who spoke badly of him. what part of the plant holds the most water Which ordered pairs in the form (x,y) are solutions to the equation?4x - 5y = 24Select each correct answer.- ( 4, 8 ) - ( 1 -4 ) - ( 6, 0 ) - ( -9, -12 ) pretty sure its easy but i cant- Which statement is true about y = arctanx?The domain is (-pi/2,pi/2)The range is all real numbers.The graph contains vertical asymptotes.The graph is symmetric about the origin. What type of cell transport is shown in the figure below?Facilitated diffusionActive transportEndocytosisSimple diffusion