Leon Bishop

2023-04-01

Construct all random samples consisting three observations from the given data. Arrange the observations in ascending order without replacement and repetition.
86 89 92 95 98.

Zackary Daugherty

To construct all random samples consisting of three observations from the given data (86, 89, 92, 95, 98), we need to arrange the observations in ascending order without replacement and repetition.
Let's list out all the possible combinations:
$\left(86,89,92\right)$
$\left(86,89,95\right)$
$\left(86,89,98\right)$
$\left(86,92,95\right)$
$\left(86,92,98\right)$
$\left(86,95,98\right)$
$\left(89,92,95\right)$
$\left(89,92,98\right)$
$\left(89,95,98\right)$
These are all the possible combinations of three observations from the given data, arranged in ascending order without replacement and repetition.
Therefore, the random samples consisting of three observations are:
$\left(86,89,92\right),\left(86,89,95\right),\left(86,89,98\right),\left(86,92,95\right),\left(86,92,98\right),\left(86,95,98\right),\left(89,92,95\right),\left(89,92,98\right),\left(89,95,98\right)$

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