Arithmetic mean

Some of you might say that solution is $\dfrac{4+5.21}{2}=4.605$ . This is wrong.

In the first set, there are $21$ numbers and the average is $4$ . That means that the sum of the numbers in the first set is $(21)(4)=84$ . It follows that the sum of the numbers in the second set is $(100)(5.21)=521$ . The total sum of numbers in the $2$ sets is $84+521=605$ . The average is total sum divided by the total numbers.

$average=\dfrac{605}{21+100}=\dfrac{605}{121}=$ $\boxed{5}$ $\large\color{#D61F06}\boxed{answer}$