What is the best alternative to Microsoft Power BI on iPhone?

Tableau Mobile, S tier, #2 in data analysis.

Is there a free alternative to Microsoft Power BI?

Yes: Tableau Mobile (S tier, #2) is free, with no in-app purchases.

No. Microsoft Power BI is #1 in data analysis.

Microsoft Power BI is S tier, #1 of the 6 tiered apps in data analysis. Here is everything that competes with it on iPhone, in tier order.

2
Tableau MobileS
Free download · ★ 4.6 · 5,693 ratings · score 91
Mobile app for viewing and interacting with Tableau dashboards from a Tableau Server or Tableau Cloud account.
3
Microsoft ExcelA
Free + IAP · ★ 4.7 · 7,568,768 ratings · score 84
Spreadsheet app for viewing, editing and analysing data, with charts, budgeting templates and sharing.
4
Google AnalyticsA
Free download · ★ 4.7 · 31,855 ratings · score 82
Free Business app for monitoring website and app performance and key metrics from a phone.
5
Vernier Graphical AnalysisB
Free download · ★ 2.4 · 729 ratings · score 71
Collects, graphs, and analyzes data from Vernier sensors, with manual entry also available for science students.
6
DataAnalysisLiteD
Free download · ★ 3.9 · 9 ratings · score 53
Plots and fits x, y data on iPhone, with curve fitting, standard curve prediction, and kinetic data analysis.

What is the best alternative to Microsoft Power BI on iPhone?: Tableau Mobile, S tier, #2 in data analysis.
Is there a free alternative to Microsoft Power BI?: Yes: Tableau Mobile (S tier, #2) is free, with no in-app purchases.
Does anything rank above Microsoft Power BI?: No. Microsoft Power BI is #1 in data analysis.