The '2016 Norton Cyber Security Insights Report: Family Edition' found 40 per cent of Indian parents saying they allowed their children to access the Internet before age 11.
However, more than half (54 per cent) of Indian parents believed their children are more likely to be bullied online than on a playground, it added.
"Cyberbullying is a growing issue and parents are struggling to identify and respond to this threat. A concern for many parents is that cyberbullying doesn't stop when their child leaves school - as long as your child is connected to a device, a bully can connect to them," Norton by Symantec Country Manager Ritesh Chopra told PTI.
"They were also worried that the children may do something online that makes the whole family vulnerable (62 per cent) or embarrassed (60 per cent)," Chopra said.
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The report also found that countries where parents had the strictest preventative measures in place, had the lowest incidence of cyberbullying.
It also found that 7 per cent of parents fail to take any action to protect their children online.
Signs of cyberbullying include children appearing nervous when they receive a text/online message or email, becoming defensive/secretive about online activity, withdrawal from friends and family, physical symptoms like trouble sleeping, stomach aches, headaches, and weight loss or gain and falling behind in school or acting out.
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