There are two different types of surveys in my opinion. There are surveys where you ask your audience about them (that is often used in a media kit) and the other survey where you ask them about your show.
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Audience Surveys About Them
This is the survey that you need demographics. So this might be things like:
Total household income
Do you own or rent
Do you have children
What products do you plan on purchasing in the future
What was the last product you purchased
Audience Surveys About You
How did you hear about the show?
How do you listen to podcasts?
How many episodes have you listened to?
Where do you listen to the podcast
Opinion on Length of Show
Opinion on ads
What is their Favorite thing about the show
What is their least Favorite
What would you like to see on the show
How likely are you to tell a friend
How much of the episode do you listen to?
Add Information About Podcasting
In some cases, this may be the first time someone is spending advertising money on a podcast. You can find great stats about the podcast industry and the podcast consumer at www.edisonresearch.com
Tips on Making Podcast Surveys
If you do anything with ratings, make the rating system even. For example on a scale from 1-4 where four is perfect and one is awful, how would you rate the length of this show? Why even? because if it was 1-5, you could choose three which is right in the center. When the numbers are even, the audience member has to pick a little better or a little worse.
Give them a bribe. I've heard of people doing surveys who say when they get X amount responses they will pull one lucky winner and they will win an Amazon GIft certificate. I once gave away a year subscription at the School of Podcasting. The bottom line is you will get 3% of your audience if you are lucky so you need a bribe. Another key point if you are asking about the length of the podcast, you can't announce the survey at the end of the show (as anyone who thought it was too long has already stopped listening).
I have a friend who works for Gallop (you know, the polling people) and he says having more than 15 questions is a waste of time. With this in mind, figure out what you really want to know and ask those questions.
There are places like Survey Monkey, and Poll Daddy, but for me, I like the free Google Forms. You can create your own questions, and then download the answers in a spreadsheet. You are not limited to any number of responses or questions.