I just wrote this up. You could stick it in a plugin if you like, or however you want to use it.
function show_statistics_info() {
global $wpdb, $table_prefix;
// get number of posts
$result = "SELECT COUNT(*) FROM {$table_prefix}posts WHERE post_status = 'publish'";
$num_posts = $wpdb->get_var($result);
// get number of categories
$result = "SELECT COUNT(*) FROM {$table_prefix}categories";
$num_cats = $wpdb->get_var($result);
// get date of oldest post
$last_post = $wpdb->get_results("
SELECT post_date
FROM {$table_prefix}posts
WHERE post_status = 'publish'
ORDER BY post_date ASC
LIMIT 1
");
// calculate dates
$num_seconds = time() - strtotime($last_post[0]->post_date);
$num_months = $num_days / (365/12); // approximate
$num_months = round($num_months);
echo "There are $num_posts number of posts in $num_cats categories over the last $num_months months.";
}