Always "in the first/second/third etc. place. In the examples you give "there" is optional.
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Shadokwhen describing a chart or a graph. Do we say :You wouldn't say "place" in describing a chart or a graph. Things are on the chart or on the graph, but within the chart, you may depict any number of things, and you would refer to these specific things, not to a "place"
In the first/second place...
or
On the first/third place...