Question

Because the mean is very sensitive to extreme values, 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 for cans that are 0.0111 in. thick. Identify any outliers, then compare the median, mean, 10% trimmed mean, and 20% trimmed mean.
248 260 267 273 276 278 282 284 284 285
287 287 290 290 293 295 296 299 311 501

Answer 1

Explanation:

Outliers: In this data set, the value of 501 is an outlier as it is significantly higher than the other values.

Median: To find the median, we arrange the data in order and find the middle value. In this case, since there are an odd number of values, the median is the middle value: 290.

Mean: To find the mean, we add up all the values and divide by the number of values:

(248 + 260 + 267 + ... + 311 + 501) / 21 = 293.67

10% Trimmed Mean: To find the 10% trimmed mean, we delete the bottom 10% of the values (2 values) and the top 10% of the values (2 values) and then find the mean of the remaining values:

(278 + 282 + 284 + 284 + 285 + 287 + 287 + 290 + 290 + 293 + 295 + 296 + 299 + 311) / 15 = 286.87

20% Trimmed Mean: To find the 20% trimmed mean, we delete the bottom 20% of the values (4 values) and the top 20% of the values (4 values) and then find the mean of the remaining values:

(284 + 284 + 285 + 287 + 287 + 290 + 290 + 293 + 295 + 296 + 299 + 311) / 12 = 288.92

The median, mean, 10% trimmed mean, and 20% trimmed mean can be compared to see how resistant each measure is to outliers. The median is the most resistant measure as it only considers the middle value, whereas the mean is the least resistant measure as it considers all values in the data set. The trimmed means are intermediate measures that are more resistant to outliers than the mean but less resistant than the median. In this case, we can see that the 10% trimmed mean is more resistant to outliers than the mean but less resistant than the 20% trimmed mean.