91影视

The axial loads of aluminum cans, which are 0.0111 inches thick, are known in pounds.

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

Outliers are those specific sets of observations that are quite different in measure compared to the rest of the data.

By observing the data, the value of 504 pounds is vastly different from other values.

Thus, the value 504 pounds is an outlier.

A median is computed using the following steps.

• Sort the data in ascending order.
• For even counts of observation, the average of two middle values gives the median.
• For odd counts of observation, the middle value gives the median.

The data is sorted as follows.

The number of observations is 20.

The middlemost observations are 285 and 286.

The median of the dataset is

$$\begin{gathered} M=\frac{285+286}{2} \\ =\frac{571}{2} \\ =285.5. \end{gathered}$$

Thus, the median is 285.5 pounds.

The formula for the mean of n observations is shown below.

$\stackrel{炉}{x}=\frac{鈭�x}{n}$

Substitute the values as follows.

$$\begin{gathered} \stackrel{炉}{x}=\frac{247+260+268+...+504}{20} \\ =\frac{5887}{20} \\ =294.35 \end{gathered}$$

Thus, the mean value is 294.4 pounds.

The 10% trimmed mean is the mean value obtained after deleting the top and bottom 10% values in the data set.

The 10% of 20 observations is

$$\begin{gathered} 10\%\text{of}20=0.1脳20 \\ =2. \end{gathered}$$

Delete the bottom and top 2 values from the data set.

The mean of these observations is computed as follows.

$$\begin{gathered} \stackrel{炉}{x}=\frac{268+273+...+299}{16} \\ =\frac{4566}{16} \\ =285.375 \end{gathered}$$

Thus, the 10% trimmed mean value is 285.4 pounds.

The 20% trimmed mean is the mean value obtained after deleting the top and bottom 20% values in the data set.

The 20% of 20 observations is

$$\begin{gathered} 20\%\text{of}20=0.2脳20 \\ =4. \end{gathered}$$

Delete the bottom and top four values from the data set.

The mean of the observations is computed as follows.

$$\begin{gathered} \stackrel{炉}{x}=\frac{276+279+...+295}{12} \\ =\frac{3430}{12} \\ =285.833 \end{gathered}$$

Thus, the 20% trimmed mean value is 285.8 pounds.

The summarized results are shown below.

As per the results, there is only one outlier. The two measures of the center (median and mean) vary largely from the complete set of observations (285.5 and 294.34 ).

But the two trimmed mean measures are almost the same and close to the median value of 285.5.

Thus, it can be observed that the inclusion of the extreme value leads to significant diversion in the mean value. It means that the measure is not resistant to the outliers.

Also, the median value is resistant, so it does not change much and is comparable to the mean values, exclusive of extreme values.