View the number of entries recorded per day

Question

The easiest way is by using custom MySQL query with WPDB class.

global $wpdb;
$table = $wpdb->prefix . 'posts';
$sql = "SELECT DATE(post_date) AS date, COUNT(ID) AS count 
    FROM {$table} WHERE post_type="my_post_type" AND post_status="publish" GROUP BY DATE(post_date)";
$rows = $wpdb->get_results($sql);

Or if you want to prevent SQL injection, you can use prepared statement like this:

global $wpdb;
$sql = $wpdb->prepare(
    "SELECT DATE(post_date) AS date, COUNT(ID) AS count 
    FROM %s WHERE post_type = %s AND post_status="publish" GROUP BY DATE(post_date)",
    array(
        $wpdb->prefix . 'posts',
        'my_post_type'
    )
);
$rows = $wpdb->get_results($sql);

Then you can iterate the $rows to show the data.

foreach ($rows as $row) {
    echo $row->date . ' -- ' . $row->count;
}