If the sum of 15 data points is 2100 and all the data is doubled and then 10…

When every value in a data set is changed by a fixed linear rule — multiplied by a constant k and then shifted by a constant c, so each new value equals k times the old value plus c — the average of the data set changes by exactly the same rule: New Average equals k times Old Average plus c. This holds because the sum of the transformed values is k times the old sum plus c times the count of values, and dividing by the same count preserves this exact relationship.

1. Find the old average: the sum of the 15 data points is 2100, so Old Average equals 2100 divided by 15, which is 140.

2. Identify the transformation applied to each data point: doubled first, then 10 subtracted, so New Value equals 2 times the old value, minus 10 — meaning k equals 2 and c equals minus 10.

3. Apply the transformation rule to the average: New Average equals 2 times Old Average minus 10, equals 2 times 140 minus 10, equals 280 minus 10, equals 270.

4. Find the required difference: New Average minus Old Average equals 270 minus 140, equals 130.

Cross-check using an independent method built from sums: New Sum equals 2 times the old sum, minus 10 times the count, equals 2 times 2100, minus 10 times 15, equals 4200 minus 150, equals 4050. New Average equals 4050 divided by 15, equals 270 — matching the value found above and confirming the difference of 130.

The new average exceeds the old average by 130.