Taken 2--and its forthcoming sequel Taken 3--are both rated PG-13. (AP Photo/20th Century Fox, Magali Bragard)

Are PG-13 movies really appropriate for teenagers? A new study puts fresh scrutiny on the movie industry's largest ratings category, showing that parents who were repeatedly exposed to violence and sexual content became progressively more accepting of the material.

That may explain what researchers describe as "ratings creep," the growing rate of violent and sexual scenes in PG-13-rated movies, many of which contains more images of gun violence than even R-rated films.

QUIZ: R or PG-13: Can you guess what these movies were rated?

"We need people to think about what is happening here with the huge increase in violence in movies and if this is harmful," said Dan Romer, a co-author of the report "Parental Desensitization to Violence and Sex in Movies," which was also published by the American Academy of Peditratics' publication, Pediatrics.

In the study, 1,000 parents were randomly shown several short clips with violence and explicit sexual content from top-grossing movies such as "8 Mile," "Die Hard," and "Taken 2." Early in their viewing, parents said the movies were only appropriate for older audiences and on average the films were appropriate for viewers 17 years old. But the more clips the parents watched, the more they began to assign lower ages and ended up saying most of the material was appropriate for PG-13 audiences.

What that could mean, Romer said, is that parents become desensitized to the mature content after repeated exposure. And this is significant, because it's often parents who watch movies and assign MPAA ratings in the first place.

The MPAA declined to comment for the story but has pointed to some academics and studies that show parents have indeed become more tolerant of mature content over time, a reflection of evolving cultural attitudes.

The PG-13 rating was first created in 1984 after parents complained about violence and gruesome scenes from movies such as "Indiana Jones and the Temple of Doom." The idea was that too many PG movies were creeping closer to being like R-rated films. So the MPAA added a new category forPG-13 films, with the label: "Parents Strongly Cautioned – Some Material May Be Inappropriate for Children Under 13."

In the last three decades, PG-13 movies have become the biggest and most profitable category for Hollywood.

According to Rentrak movie research firm, more movies have been rated PG-13 than any other rating every year since 2008 have been PG-13 movies. The category has consistently grown each year as the PG and R category slowly shrink. In 1999, 35 percent of top movies were rated PG-13. Last year, 47 percent were PG-13 and only one film was rated G.

But for many parents, the PG-13 rating is too broad. Movie studios draw limited audiences for G and PG films, with kids wanting to see the hottest action films, such as PG-13 rated "Guardians of Galaxy." R-rated films have pushed the edge of their rating too, deleting just enough content to be appropriate for teens.

The new study comes amid fresh criticism that Hollywood has neglected family-friendly movies. Last year, Romer published a study that showed the amount of gun violence in PG-13 has has tripled since 1985 and in 2012 the category had more gun violence than R-rated films.

Childrens' media advocacy group Common Sense Media earlier this month announced it would give its own seal of approval for "family-friendly" films. In cooperation with Disney, the group gave "Alexander and the Terrible, Horrible, No Good, Very Bad Day," its first seal, which will appear on DVD cases.

The group came up with the seal because it said too often parents took their children to films and were surprised by violence, mature language and sexual content they found in the films.

"We don't see enough great movies with positive role models and messages that make parents feel like a trip to the movies is time well spent together -- and we think families deserve better," said Jim Steyer, founder and chief executive of Common Sense, in a statement. "The Common Sense Seal will recognize the best in family movies with a goal of inspiring studios to create more films that kids and parents can enjoy together."

Now, take our quiz to see if you can guess how these hit movies were rated.