“I have the No. 1 show on NBC.”

No one ever accused Donald Trump of being modest. So when he was asked in a combative Today show interview when he would formally announce a campaign for president, the tycoon said he was being respectful of NBC.

After all, Trump said, his show The Celebrity Apprentice is the network’s top-rated show.

Here’s the exchange with Today host Meredith Vieira:

Vieira: “What are you waiting for?”

Trump: “I hate to say it, I have the No. 1 show on NBC. Is that a correct statement? I mean, The Apprentice is doing great — The Celebrity Apprentice.”

Vieira: “What does that have to do….”

Trump: “It has a lot to do. It sounds so trivial, and I hate to even bring it up, but I’m not allowed to run during the show. You’re not allowed to have the show on and be a declared candidate. It’s a great show and it’s got phenomenal ratings, and until that show is over, I can’t declare, because otherwise, NBC would have to take the show off the air, and I think that would be very unfair to NBC.”

This season’s Celebrity Apprentice is the latest in a long-running NBC reality show that features celebrities ranging from a country singer to a Playmate of the Year competing in a series of challenges that include creating a children’s book and selling pizzas. At the end of each show, one of them gets fired by Trump.

So how do the ratings look? It depends whether you’re referring to recent weeks or to the entire season.

If you look at the most recent week’s Nielsen ratings, Trump is right. For the week ending April 3, 2011, The Celebrity Apprentice ranked higher than any NBC prime time broadcast show among adults age 18-49 — the coveted demographic for television executives.

We should note that the bar is pretty low to be the highest-rated NBC show these days. When you consider shows on all broadcast networks that week, The Celebrity Apprentice ranked 15th. And The Celebrity Apprentice was the only NBC show to rank in the top 22 — behind 10 from CBS, eight from ABC and three from Fox.

We’ll also note that for the previous week — the one ending March 27 — The Celebrity Apprentice finished third on NBC and 19th overall.

Still, Trump’s right for the most recent ratings.

For the entire season, however, The Celebrity Apprentice is not the top-rated NBC show.

Marc Berman, a senior television editor at AdWeek, provided us with the average Nielsen ratings for all 160 broadcast network shows between Sept. 20, 2010, and April 3, 2011 — basically, the entire season to date.

Here’s how the top NBC shows stack up for the 18-to-49 demographic:

1. Sunday Night Football (3rd overall)
2. Football Night in America pregame show (tied for 17th overall)
3. The Office (tied for 17th overall)
4. The Biggest Loser (tied for 34th overall)
5. The Celebrity Apprentice (tied for 36th overall)

And here are the numbers for all ages:

1. Sunday Night Football (4th overall)
2. Harry’s Law (29th overall)
3. Football Night in America pregame show (33rd overall)
4. Law & Order L.A. (42nd overall)
5. The Celebrity Apprentice (44th overall)

So in both categories, The Celebrity Apprentice ranks fifth behind a mix of scripted dramas, sitcoms, reality shows and Sunday football. By this standard, Trump is wrong to say he has “the No. 1 on NBC.”

“It’s misleading,” Berman said. “His show is doing well for NBC, but it’s not the No. 1.”

So Trump’s boast needs some context. He’s right for the most recent ratings, but not for the season overall. We find his claim Half True.