The average of 39 numbers is 17. Each number is multiplied by 12 and then 16 is added to each number. Finally, each number thus formed is divided by 11.
Determine the average of the new sets of numbers thus formed?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 20
When the same operation is done on every number of a set, the average changes in the same way: multiplying every number by 12 multiplies the average by 12, adding 16 to every number adds 16 to the average, and dividing every number by 11 divides the average by 11. The number of values, 39, does not matter.
Multiplied by 12: \(17\times12=204\)
16 added: \(204+16=220\)
Divided by 11: \(220\div11=20\)