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
QveST [7]
3 years ago
10

Consider the discussion in our Devore reading in this unit involving an important distinction between mean and median that uses

the concept of a trimmed mean to highlight an important continuum between the two. Presuming that the mean and median are different values for a distribution, the mean can be taken to indicate a 0% trim, and the median can be taken to approach a 50% trim (with effectively 100% of the values removed). These two values define a continuum of trimmed mean values that would fall between the two. Discuss why the mean and median of the distribution always approach each other as we take trimmed means at higher and higher percentages (e.g., 10%, 20%, 30% ...). In particular, describe what is happening to the kurtosis and skewness of the distribution as we trim off more and more data. Speculate on whether or not you might expect to see an optimum point in that process at some value between the mean and median. (Hint: You should!) Why might this matter?
Mathematics
1 answer:
Levart [38]3 years ago
3 0

Answer:

Step-by-step explanation:

A trimmed mean is a method of averaging that removes a small designated percentage of the largest and smallest values before calculating the mean. After removing the specified observations, the trimmed mean is found using a standard arithmetic averaging formula. The use of a trimmed mean helps eliminate the influence of data points on the tails that may unfairly affect the traditional mean.

trimmed means provide a better estimation of the location of the bulk of the observations than the mean when sampling from asymmetric distributions;

the standard error of the trimmed mean is less affected by outliers and asymmetry than the mean, so that tests using trimmed means can have more power than tests using the mean.

if we use a trimmed mean in an inferential test , we make inferences about the population trimmed mean, not the population mean. The same is true for the median or any other measure of central tendency.

I can imagine saying the skewness is such-and-such, but that's mostly a side-effect of a few outliers, the fact that the 5% trimmed skewness is such-and-such.

I don't think that trimmed skewness or kurtosis is very much used in practice, partly because

If the skewness and kurtosis are highly dependent on outliers, they are not necessarily useful measures, and trimming arbitrarily solves that problem by ignoring it.

Problems with inconvenient distribution shapes are often best solved by working on a transformed scale.

There can be better ways of measuring or more generally assessing skewness and kurtosis, such as the method above or L-moments. As a skewness measure (mean ? median) / SD is easy to think about yet often neglected; it can be very useful, not least because it is bounded within [?1,1][?1,1].

i expect to see the optimum point in that process at some value between the mean and median.

You might be interested in
Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are -6 and 162, respectively.
Step2247 [10]
Hello,

a(2)=-6
a(3)=-6*r
a(4)=-6*r²
a(5)=-6*r^3=162
a(5)/a(2)=r^3=162/(-6)=-27==>r=-3

a(1)=-6/(-3)=2
a(2)=2*(-3)
a(3)=2*(-3)²
a(4)=2*(-3)^3
a(5)=2*(-3)^4

a(n)=2*(-3)^(n-1)




Answer
5 0
3 years ago
Read 2 more answers
Geraldine is asked to explain the limits on the range of an exponential equation using the function f(x) = 2^x. She makes these
Dafna11 [192]

Consider the exponential function f(x)=2^x.

By definition, the domain of a function is the set of input argument values for which the function is real and defined.

Let we take x=2, then f(2)=2^2=4

x=4, then f(4)=2^4=16

x=10, then f(10)=2^{10}=1024

If we chose larger values of x, we get larger function values.

For example, If we take f(0)=2^0=1

f(-3)=2^{-3}=\frac{1}{2^3}=\frac{1}{8}

f(-10)=2^{-10}=\frac{1}{2^10}=\frac{1}{1024}

Thus if we choose smaller and smaller values of x. the f unction values will be smaller and smaller functions.

Thus the domain of the function is the set of all real numbers.

Thus the range is limited to the set of positive real numbers. That is, (0,\infty)

If we choose larger values of x, we will get larger function values, as the function values will be larger powers of 2.

If we choose smaller and smaller x values, the function values will be smaller and smaller fractions.

8 0
3 years ago
Read 2 more answers
Please solve these questions with the equations. Will give 80 points and mark brainliest to the person with the answers.
I am Lyosha [343]

1]

8(x-7)=128 \ \ /:8\\\\x-7=16 \ \ /+7\\\\\huge\boxed{x=23}

2]

16=2(x+7) \ \ /:2\\\\x+7=8 \ \ /-7\\\\\huge\boxed{x=1}

3]

\frac{7y}{7}=20\\\\\huge\boxed{y=20}

4]

2x-1=9 \ \ /+1\\\\2x=10 \ \ /:2\\\\\huge\boxed{x=5}

5]

2(x-8)=20 \ \ /:2\\\\x-8=10 \ \ /+8\\\\\huge\boxed{x=18}

5 0
3 years ago
Micheal has to walk 3/8 of a kilometer to the store. He walks 4/5 of the way. How far did he walk. ?
bonufazy [111]
144 feet until he gets to the store
7 0
3 years ago
What's the power of a power
ahrayia [7]
<span>The power of a number says how many times to use the number in a multiplication. It is written as a small number to the right and above the base number.</span>
5 0
3 years ago
Other questions:
  • In a 30-60-90 triangle, the hypotenuse is the shorter leg times the square root of two.
    11·2 answers
  • Jackson said, "I am thinking of two
    12·1 answer
  • What is 3 divided 76
    8·2 answers
  • Evaluate 3m-n when m=5 and n=1
    5·1 answer
  • Which expression are equivalent to 2x+4
    10·1 answer
  • Help me with this somebody.
    12·1 answer
  • Spinner 1 is divided into four congruent sections, and Spinner 2 is divided into three congruent sections, as shown below. Each
    13·2 answers
  • Need help somebody pleaseee
    9·1 answer
  • Simplify: -8x +7-5-5x + 5x<br> A<br> - 8x + 2<br> B<br> -18x+12<br> -x-5<br> D<br> -X+12
    8·1 answer
  • How to find the indicated angle of a triangle
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!