Question

you have collected data about the average response time of participants in your study. You are delighted to find that the variable is normally distributed. More than half your respondents tank longer than 16 seconds to respond and 1/3 take less than 12 seconds to respond. What is the median response time for your participants.

Answer 1

Lets say there are total of 100 participants arranged in increasing order of response time.

So first 1/3rd participants (1-33) will be the ones taking less than 12 seconds.

Lets say 51 participants take longer than 16 seconds (this is assumed as 51 is the lowest number which is more than half of participants). These 51 participants will be towards the end i.e. 50-100

All other participants from 34-49 will take 12-16 seconds to respond.

Now keeping this arrangement in mind, we can certainly say that median response time of the participants is more than 16 seconds because median time will be the average time of 50th and 51st participants both of which are more than 16 seconds in our case.

The answer will be same for any number of participants because its the arrangement that matters.