91影视

The sample data for the lifetime (in hours) for a certain type of component is provided.

The measures of the center that can be computed in the provided scenario are median, 20% trimmed mean and 30% trimmed mean.

The sample median is computed by first ordering the data in ascending order.

The data arranged in ascending order is as follows,

17 29 35 48 57 79 86 92 100+ 100+

For the even number of observations, the median value is computed as,

\(\begin{array}{c}\tilde x &=& average\;of\;{\left( {\frac{n}{2}} \right)^{th}}and\;{\left( {\frac{n}{2} + 1} \right)^{th}}\;ordered\;values\\ &=& average\;of\;{\left( {\frac{{10}}{2}} \right)^{th}}and\;{\left( {\frac{{10}}{2} + 1} \right)^{th}}\;ordered\;values\\ &=& average\;of\;{\left( 5 \right)^{th}}and\;{\left( 6 \right)^{th}}\;ordered\;values\\ &=& \frac{{57 + 79}}{2}\\ &=& 68\end{array}\)

Thus, the median value is 68.

Using the arranged data,

The 20% trimmed mean is computed by eliminating the smallest two and the largest two values from the data and taking the average of the rest of the data.

The 20% trimmed mean is given as,

\(\begin{array}{c}{{\bar x}_{tr\left( {20} \right)}} = \frac{{35 + 48 + 57 + ... + 92}}{6}\\ = 66.2\end{array}\)

Therefore, the 20% trimmed mean is 66.2.

The 30% trimmed mean is computed by eliminating the smallest three and the largest three values from the data and taking the average of the rest of the data.

\(\begin{array}{c}{{\bar x}_{tr\left( {30} \right)}} &=& \frac{{48 + 57 + 79 + 86}}{4}\\ &=& 67.5\end{array}\)

Therefore, the 30% trimmed mean is 67.5.