An alternative method that is more automatic but also more complex:

It uses the ability of a chart to ignore hidden cells. So if your blank cells are in hidden rows, they will not be part of the chart.
Table 2 is typed in. No formulas. The word needs to match the name in Table 1 that you want to chart.
Table 3 is made up of formulas and is filtered. As you can see it has hidden rows and is only showing the data to be charted. Make the table with as many or more rows as Table 1 has columns.
B1 =Table 2::B2
A2 =INDEX(Table 1::$1:$1,ROW())
B2 =VALUE(VLOOKUP($B$1,Table 1::$1:$3,ROW(),0)&"")
Edit that formula in B2 so it includes all rows of your table 1. I only have $1:$3.
Fill down to complete the columns
You will have error triangles at the bottom of the table if it is longer than Table 1 is wide
You will have error triangles in column B wherever there was a blank cell in Table 1.
Create your chart from this table. Use the entire table for the chart, error triangles and all.
Create a filter for the table of "show rows where column B text is not..." and type in any non-numeric text, like a space character. The table should shrink up to just the rows with data. The chart should include only those rows.
Move Table 3 to another sheet to get it out of the way. You should never have to mess with it again unless you need to add more rows to it.
Note that the formula in column B is designed around how VLOOKUP and other referencing functions will translate a blank cell into a zero. If you attach a &"" to the end, it does not do that but it makes the result text. VALUE turns it back to a number or, if it cannot, it creates an error. The filter is using that error to filter out the row.