Edit in JSFiddle

const data = {
  places: [ "geoId/05" ],
  stat_vars: [ "Count_Person_Female" ]
};
const request = new XMLHttpRequest();
request.open("POST", "https://api.datacommons.org/stat/all", false /* async */ );
request.send(JSON.stringify(data));

if (request.status == 200) {
  let result = JSON.parse(request.responseText);
  for (const place of Object.keys(result['placeData'])) {
    for (const statVar of Object.keys(result['placeData'][place]['statVarData'])) {
      console.log(`result['placeData']['${place}']['statVarData']['${statVar}']:`);
      console.log(result['placeData'][place]['statVarData'][statVar]);
    }
  }
} else {
  console.log("There was an error fetching data.");
}