Morning Afternoon Evening Avg Header
9
4
2
8.75
 Morning
8
1
3
10
2
1
8
1
1

Morning Afternoon Evening Avg Header
9
4
8
8.75
 Morning | Evening
8
1
8
10
2
11
8
1
8

Code:
let
    Source = Excel.CurrentWorkbook(){[Name="Table1"]}[Content],
    UNP = Table.UnpivotOtherColumns(Source, {}, "Header", "Value"),
    GroupAvg = Table.Group(UNP, {"Header"}, {{"Avg", each List.Average([Value]), type number}}),
    SortDsc = Table.Sort(GroupAvg,{{"Avg", Order.Descending}}),
    Group = Table.Group(SortDsc, {"Avg"}, {{"Count", each _, type table}}),
    List = Table.AddColumn(Group, "Header", each [Count][Header]),
    Extract = Table.TransformColumns(List, {"Header", each Text.Combine(List.Transform(_, Text.From), " | "), type text}),
    Max = List.Max(Extract[Avg]),
    FilterMax = Table.SelectRows(Extract, each [Avg] = Max)
in
    FilterMax
tolerates duplicates, extra columns and rows