Trimmed Mean Because the mean is very sensitive to extreme val...

Question

Trimmed Mean Because the mean is very sensitive to extreme values, we say that it is not a resistant measure of center. By deleting some low values and high values, the trimmed mean is more 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 (from Data Set 41 “Aluminum Cans” in Appendix B) for cans that are 0.0111 in. thick. An axial load is the force at which the top of a can collapses. Identify any outliers, then compare the median, mean, 10% trimmed mean, and 20% trimmed mean.

247 260 268 273 276 279 281 283 284 285 286 288
289 291 293 295 296 299 310 504

247 260 268 273 276 279 281 283 284 285 286 288

289 291 293 295 296 299 310 504

Accepted Answer

Hello, everyone. Let's take a look at this question together. A group of researchers measured the breaking strength in pounds of 20 samples of a newly designed fiber rope. The recorded strengths were recorded as follows. Compute the mean and median of the data. Find the 10% trimmed mean and the 20% trimmed mean. And here we have 4 different answer choices containing different values for the mean, the median, the 10% trimmed mean, and the 20% trimmed mean. So the first step in determining the correct answer choice is calculating the mean, where we know that the value of N is equal to 20, so there are 20 total values, and plugging in the data into the mean formula, we get 230 as the value for the mean. So the mean breaking strength is 230 pounds. Then we compute the median value. And since we have 20 total values, the median is the average of the 10th and 11th values, which from our sorted data set in ascending order, we can identify the 10th and 11th values are 230 and. 232 respectively. And since the 10th value is 230, and the 11th value is 232, the median is 231 pounds. Next, we can compute the 10% trimmed mean. Which for the 10% trimmed mean we removed the lowest 10%, which is 185 and 192, and the highest 10%, which is 270 and 278, leaving us with the following data values remaining, which we can use to compute the 10% trimmed mean. And plugging in the values into our mean formula, we get 229.7%, so the 10% trimmed mean is 2. 129.7 pounds. And lastly, we compute the 20% trimmed mean, which for the 20% trimmed mean we removed the lowest 20%, which is 185, 192, 198, and 203, and the highest 20%, which is 252, 260, 270, and 278, which leaves us with the remaining data values that we can use to calculate the 20% trimmed mean. Plugging the values into the formula for the 20% trimmed mean, giving us 230.2, so the 20% trimmed mean is 230.2 pounds. So from our calculations, we got 230 as the mean, 231 as the median. The 10% trimmed mean is 2 29.7, and the 20% trimmed mean is 230.2, which looking at our answer choices, we can identify that answer choice C is the correct answer, as answer choice C contains all of the correct values for the mean median 10% trimmed mean and 20% trimmed mean, and all other answer choices are incorrect. I hope you found this video to be helpful. Thank you and goodbye.

��app

Key Concepts

Trimmed Mean

Outliers

Measures of Central Tendency

Watch next