Código PHP:
Ver original echo "<tr>";
echo "\n<input type=hidden name='nombre$i' value='" . $fila["nombre"] . "'>";
echo "<td>" . $fila["nombre"] . "</td>";
echo "<td><input type=text name='calif1' size='5' value='" . $fila["calif1"] . "' ></td>";
echo "<td><input type=text name='calif2' size='5' value='" . $fila["calif2"] . "' ></td>";
echo "<td><input type=text name='calif3' size='5' value='" . $fila["calif3"] . "' ></td>";
$promedio = ($fila["calif1"] + $fila["calif2"] + $fila["calif3"]) / 3;
echo "<td><input type=text name='promedio' value='$promedio' MAXLENGTH='3' size='5' ></td>";
echo "</tr>";
$i++;
}
intenta algo asi
saludos!