Is the mode always at the centre of the data ?

When the open organ pipe resonates in its fundamental mode then at the centre of the pipe

Find the missing frequency f for the following data if the mode for the data is 39 : {:("Class ",5-15,15-25,25-35,35-45,45-55,55-65,65-75),("Frequency "," "2," "3," "f," "7," "4," "2," "2):}

Find the mean and variance for each of the data :

Find the mean and variance for each of the data :

A horse is tied to a post by a rope. If the horse moves along a circular path always keeping the rope tight and describes 88 m when it has traced out 54^(@) at the centre. Find the length of the rope.