A few days before Christmas, it was clear Amazon.com's (NASDAQ:AMZN) voice-activated smart speakers were a hit. The e-commerce giant's artificial intelligence home devices sold out on the company's website the weekend before Christmas "due to high demand," management said in a statement. But with the full holiday season now behind us, Amazon is back with a more robust update on how successful the new device, and Amazon's overall e-commerce business, were during the biggest shopping period of the year.

Amazon Echo

The Amazon Echo. Image source: Amazon.

Powered by Alexa, the company's AI introduced in 2014, the company's flagship Alexa-enabled Echo speaker and its smaller Echo Dot stole the show at Amazon this year. And the company's impressive holiday performance didn't stop at its Alexa devices. In 10 wild facts, here's a closer look at Amazon's crushing holiday season:

1. Despite Amazon's "best efforts and ramped-up production," it said in a press release on Tuesday, the company still couldn't keep the Echo or Echo Dot in stock.

2. Orders for Amazon's Echo -- the company's flagship $180 smart speaker -- are still backed up significantly. At the time of this writing, the company's website says the black Echo won't be in stock until Jan. 26 and its white Echo won't be available until Jan. 20.

3. Record-setting orders of Amazon Echo family devices were up more than 900% compared to last year's holiday season.

4. "Millions" of Alexa devices were sold worldwide this year, Amazon said in its Tuesday press release, though the company refrained from specifying a more precise number.

5. Over a billion Prime and "Fulfillment by Amazon" items were shipped globally during the holiday season.

6. The number of Prime members is at a record high.

7. Over 72% of Amazon customers shopped on a mobile device, up from 70% last holiday season.

8. Shopping via Amazon's mobile app soared 56% compared to the year-ago period -- big growth on top of last holiday season's year-over-year growth of more than 100%.

9. On Cyber Monday, Amazon customers purchased an average of 46 electronics items per second, up from 33 per second on Cyber Monday last year.

10. Prime Now, Amazon's free one- and two-hour delivery available in some metro areas, saw considerable momentum. Prime Now worldwide deliveries and orders were up more than 300%, the company said.

Amazon Fulfillment Center Amzn Stock

Amazon fulfillment center. Image source: Amazon.

These impressive facts about Amazon's peak holiday season, which the company says begins on Nov. 1, bode well for the company's overall fourth-quarter results. When Amazon reported third-quarter financial results, management said it expected fourth-quarter revenue to be between $42 billion and $45.5 billion, representing 17% to 27% year-over-year growth. Considering Amazon's third-quarter revenue was up 29% year over year, investors may be hoping the company's holiday-driven fourth-quarter net sales growth is at the high end of management's guidance.

Investors should learn more when Amazon reports fourth-quarter results. The company usually reports financial performance for its fourth quarter toward the end of January.

Daniel Sparks has no position in any stocks mentioned. The Motley Fool owns shares of and recommends Amazon.com. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.