Question

resistant. To find the​ 10% trimmed mean for a data​ set, first arrange the data in​ order, then delete the bottom​ 10% of the values and delete the top​ 10% of the​values, then calculate the mean of the remaining values. Use the axial loads​ (pounds) of aluminum cans listed below for cans that are 0.0111 in. thick. Identify any​outliers, then compare the​ median, mean,​ 10% trimmed​ mean, and​ 20% trimmed mean.

247247

261261

269269

272272

275275

279279

280280

284284

285285

285285

 

285285

288288

289289

292292

292292

295295

295295

300300

311311

504504

Identify any outliers. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A.

The​ outlier(s) is/are

 

nothing

pounds.

​(Type a whole number. Use a comma to separate answers as​ needed.)

B.

There are no outliers.

The median is

 

nothing

pounds.

​(Type an integer or decimal rounded to one decimal place as​ needed.)

The untrimmed mean is

 

nothing

pounds.

​(Type an integer or decimal rounded to one decimal place as​ needed.)

The​ 10% trimmed mean is

 

nothing

pounds.

​(Type an integer or decimal rounded to one decimal place as​ needed.)

The​ 20% trimmed mean is

 

nothing

pounds.

​(Type an integer or decimal rounded to one decimal place as​ needed.)

Compare the values. Choose the correct answer below.

A.

The​ median, untrimmed​ mean, and​ 10% trimmed mean are close to each other.​ However, the​ 20% trimmed mean is significantly different from those values.

B.

The​ median, untrimmed​ mean, and​ 20% trimmed mean are close to each other.​ However, the​ 10% trimmed mean is significantly different from those values.

C.

All of the values are close to each other.

D.

The untrimmed​ mean, 10% trimmed​ mean, and​ 20% trimmed mean are close to each other.​ However, the median is significantly different from those values.

E.

The​ median, 10% trimmed​ mean, and​ 20% trimmed mean are close to each other.​ However, the untrimmed mean is significant

Answer 1

Solution:

Identify any outliers. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

Answer: A. The outliers are:

The median is:

The untrimmed mean is

Therefore, the untrimmed mean is 294.4

The​ 10% trimmed mean is

To find the 10% trimmed mean, we have to delete bottom 10% of data and top 10% of data. That is we have to delete first 2 observations and last 2 observations.

The 20% trimmed mean is:

To find the 20% trimmed mean, we have to delete bottom 20% of data and top 20% of data. That is we have to delete first 4 observations and last 4 observations.

Compare the values. Choose the correct answer below.

Answer: The correct answer is:

E. The​ median, 10% trimmed​ mean, and​ 20% trimmed mean are close to each other.​ However, the untrimmed mean is significant