1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Grace [21]
3 years ago
8

Each of the following data sets has a mean of x = 10. (i) 8 9 10 11 12 (ii) 7 9 10 11 13 (iii) 7 8 10 12 13 (a) Without doing an

y computations, order the data sets according to increasing value of standard deviations. (i), (iii), (ii) (ii), (i), (iii) (iii), (i), (ii) (iii), (ii), (i) (i), (ii), (iii) (ii), (iii), (i) (b) Why do you expect the difference in standard deviations between data sets (i) and (ii) to be greater than the difference in standard deviations between data sets (ii) and (iii)? Hint: Consider how much the data in the respective sets differ from the mean. The data change between data sets (i) and (ii) increased the squared difference ÎŁ(x - x)2 by more than data sets (ii) and (iii). The data change between data sets (ii) and (iii) increased the squared difference ÎŁ(x - x)2 by more than data sets (i) and (ii). The data change between data sets (i) and (ii) decreased the squared difference ÎŁ(x - x)2 by more than data sets (ii) and (iii). none of the above
Mathematics
1 answer:
stepladder [879]3 years ago
6 0

Answer:

Step-by-step explanation:

Given are 3 data sets with values as:

(i) 8 9 10 11 12   ... Mean =10

(ii) 7 9 10 11 13    ... Mean =10

(iii) 7 8 10 12 13   ... Mean =10

We see that  data set shows mean deviations as

(i) -2 -1 0 1 2  

(ii) -3 -1 0 1 3    

(iii) -3 -2 0 2 3  

Since variance is the square of std deviation, we find that std deviation is larger when variance is larger.

Variance is the sum of squares of (x-mean).  Whenever x-mean increases variance increases and also std deviation.

Hence we find that without calculations also (i) has least std dev followed by (ii) and then (iii)

(i) (ii) (iii) is the order.

b) Between (i) and (ii) we find that 3 entries are the same and 2 entries differ thus increasing square by 9-4 twice.  But between (ii) and (iii) we find that

increase in square value would be 4-1 twice. Obviously the latter is less.

You might be interested in
Use the Fundamental Theorem for Line Integrals to find Z C y cos(xy)dx + (x cos(xy) − zeyz)dy − yeyzdz, where C is the curve giv
Harrizon [31]

Answer:

The Line integral is π/2.

Step-by-step explanation:

We have to find a funtion f such that its gradient is (ycos(xy), x(cos(xy)-ze^(yz), -ye^(yz)). In other words:

f_x = ycos(xy)

f_y = xcos(xy) - ze^{yz}

f_z = -ye^{yz}

we can find the value of f using integration over each separate, variable. For example, if we integrate ycos(x,y) over the x variable (assuming y and z as constants), we should obtain any function like f plus a function h(y,z). We will use the substitution method. We call u(x) = xy. The derivate of u (in respect to x) is y, hence

\int{ycos(xy)} \, dx = \int cos(u) \, du = sen(u) + C = sen(xy) + C(y,z)  

(Remember that c is treated like a constant just for the x-variable).

This means that f(x,y,z) = sen(x,y)+C(y,z). The derivate of f respect to the y-variable is xcos(xy) + d/dy (C(y,z)) = xcos(x,y) - ye^{yz}. Then, the derivate of C respect to y is -ze^{yz}. To obtain C, we can integrate that expression over the y-variable using again the substitution method, this time calling u(y) = yz, and du = zdy.

\int {-ye^{yz}} \, dy = \int {-e^{u} \, dy} = -e^u +K = -e^{yz} + K(z)

Where, again, the constant of integration depends on Z.

As a result,

f(x,y,z) = cos(xy) - e^{yz} + K(z)

if we derivate f over z, we obtain

f_z(x,y,z) = -ye^{yz} + d/dz K(z)

That should be equal to -ye^(yz), hence the derivate of K(z) is 0 and, as a consecuence, K can be any constant. We can take K = 0. We obtain, therefore, that f(x,y,z) = cos(xy) - e^(yz)

The endpoints of the curve are r(0) = (0,0,1) and r(1) = (1,π/2,0). FOr the Fundamental Theorem for Line integrals, the integral of the gradient of f over C is f(c(1)) - f(c(0)) = f((0,0,1)) - f((1,π/2,0)) = (cos(0)-0e^(0))-(cos(π/2)-π/2e⁰) = 0-(-π/2) = π/2.

3 0
3 years ago
When you run your average step length is 42 inches. How many steps would you have to take to run 1 mile 5(,280 feet)?
Katarina [22]

Answer:

1 508.57143 steps

Step-by-step explanation:

divide 5,280 feet by 42 inches to get 1 508.57143 steps.

3 0
3 years ago
In this figure what is m 5?​
Harlamova29_29 [7]

Answer:

m<5 = 95 degrees

Step-by-step explanation:

Let's first find m<1

=> m<1 = 180-85

=> m<1 = 95 degrees

Since,

m<1 = m<5 (Corresponding angles)

So,

m<5 = 95 degrees

3 0
2 years ago
If the ratio of the purple flowers to black flowers is 4 to 8 and there are a total of 108 flowers, how many of the flowers are
tankabanditka [31]
There would be 36 purple flowers.
7 0
3 years ago
Find the value of c such that y= x + c is a tangent to the parabola y = x squared - x - 12
Bond [772]

Answer:

c = –13

Step-by-step explanation:

by property of tangent line, equation

x² – x – 12 = x + c

x² – 2x – 12 – c = 0

has only one solution, which mean

– 12 – c = 1

c = –13

5 0
3 years ago
Other questions:
  • Suppose a certain baseball diamond is a square 65 feet on a side. The pitching rubber is located 41.5 feet from home plate on a
    13·1 answer
  • Just a lil some some so please help me
    6·2 answers
  • PLSSS HELP!! For the given ordered pairs, write a function rule relating x and y. (1,4), (2,9), (3,16), (4,25)​
    9·1 answer
  • Tamara finds the sum of two number cubes rolled at the same time. The chart below shows all possible sums from the 36 possible c
    14·1 answer
  • The hypotenuse of a right triangle is three times the length of its first leg. The length of the other leg is four feet. Find th
    12·1 answer
  • In a school of 1800 students, the ratio of teachers to students is 1:20. Some teachers join the school and the ratio changes to
    12·1 answer
  • Place a check mark next to each equivalent expression
    14·1 answer
  • Can someone help please??
    7·1 answer
  • Any ideas on this one?
    11·2 answers
  • easy ratio questions !! - giving brainly if correct and both questions are answered :) question in the file ^​
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!