DataTables

HTML

<link rel="stylesheet" href="https://cdn.datatables.net/r/dt/dt-1.10.9/datatables.min.css">
<script src="https://cdn.datatables.net/r/dt/dt-1.10.9/datatables.min.js"></script>
<label><input id="47y" type="checkbox">47 years</label>
<label><input id="51y" type="checkbox">51 years</label>
<hr>
<table id="example" class="display" cellspacing="0" width="100%">
  <thead>
    <tr>
      <th>Name</th>
      <th>Position</th>
      <th>Office</th>
      <th>Age</th>
      <th>Start date</th>
      <th>Salary</th>
    </tr>
  </thead>
  <tfoot>
    <tr>
      <th>Name</th>
      <th>Position</th>
      <th>Office</th>
      <th>Age</th>
      <th>Start date</th>
      <th>Salary</th>
    </tr>
  </tfoot>
  <tbody>
    <tr>
      <td>Tiger Nixon</td>
      <td>System Architect</td>
      <td>Edinburgh</td>
      <td>61</td>
      <td>2011/04/25</td>
      <td>$320,800</td>
    </tr>
    <tr>
      <td>Garrett Winters</td>
      <td>Accountant</td>
      <td>Tokyo</td>
      <td>63</td>
      <td>2011/07/25</td>
      <td>$170,750</td>
    </tr>
    <tr>
      <td>Ashton Cox</td>
      <td>Junior Technical Author</td>
      <td>San Francisco</td>
      <td>66</td>
      <td>2009/01/12</td>
      <td>$86,000</td>
    </tr>
    <tr>
      <td>Bradley Greer</td>
      <td>Software Engineer</td>
      <td>London</td>
      <td>41</td>
      <td>2012/10/13</td>
      <td>$132,000</td>
    </tr>
    <tr>
      <td>Dai Rios</td>
      <td>Personnel Lead</td>
      <td>Edinburgh</td>
      <td>35</td>
      <td>2012/09/26</td>
      <td>$217,500</td>
    </tr>
    <tr>
      <td>Jenette Caldwell</td>
      <td>Development Lead</td>
      <td>New York</td>
      <td>30</td>
      <td>2011/09/03</td>
      <td>$345,000</td>
    </tr>
    <tr>
      <td>Yuri Berry</td>
      <td>Chief Marketing Officer (CMO)</td>
      <td>New York</td>
      <td>40</td>
      <td>2009/06/25</td>
      <td>$675,000</td>
    </tr>
    <tr>
      <td>Caesar Vance</td>
      <td>Pre-Sales Support</td>
  ...

JavaScript

$(document).ready(function() {
  var table = $('#example').DataTable();

  /*    
      $('#47y, #50y').on('click', function(){
      var checked = $(this).is(':checked');
      $('#47y, #50y').attr('checked', checked);
  });
    */

  $('input[type="checkbox"]').on('change', function() {
    console.log($(this).attr("id"), this.checked)
    var choosedString = "";
    if ($('#47y').prop('checked')) {
      choosedString = "47"
    }
    if ($('#51y').prop('checked')) {
      choosedString += choosedString.length > 0 ? "|" : "";
      choosedString += "51"
    }
    console.log(table)
    table.column(3).search(choosedString,  true, false).draw();

  });






});