SOURCE

function getData(){
var ul = document.querySelector("#source");
var data = [];
for(var i=0; i < ul.children.length; i++){
	var li = ul.children[i];
	//console.log(li_text);
	var b = li.getElementsByTagName("b")[0];
	var air_quality = b.firstChild.nodeValue;
	var li_text = li.firstChild.nodeValue;
	var pattern = /(.+)空气/;
	var text = li_text.match(pattern)[1];
	//var data_item = [text, parseInt(air_quality)];
	var data_item = [text, air_quality];
	
	data.push(data_item);
}
	return data	
}

function sortAqiData(data) {
	function compare(value1, value2){
	return value1[1]-value2[1];
}
	data.sort(compare);
	return data;
}
function render(data) {
	var list = document.getElementById("resort");
    for(var i=0; i<data.length; i++){                                                                                                           
          var li = document.createElement("li");
          var text_content = "第"+(i+1)+"名: "+data[i][0]+", "+data[i][1];
          var text = document.createTextNode(text_content);
          li.appendChild(text);
		  list.appendChild(li);
	  }
}
function btnHandle() {
  var aqiData = getData();
  aqiData = sortAqiData(aqiData);
  render(aqiData);
}
function init() {
	var button = document.getElementById("sort-btn");
	console.log(button)
	button.onclick = function(){
		btnHandle();
	}
};
init();

<ul id="source">
    <li>北京空气质量：<b>90</b></li>
    <li>上海空气质量：<b>70</b></li>
    <li>天津空气质量：<b>80</b></li>
    <li>广州空气质量：<b>50</b></li>
    <li>深圳空气质量：<b>40</b></li>
    <li>福州空气质量：<b>32</b></li>
    <li>成都空气质量：<b>100</b></li>
  </ul>

  <ul id="resort">
    <!-- 
    <li>第一名：北京空气质量：<b>90</b></li>
    <li>第二名：北京空气质量：<b>90</b></li>
    <li>第三名：北京空气质量：<b>90</b></li>
     -->

  </ul>

  <button id="sort-btn">排序</button>