Marks obtained by some students of a class are 36, 37, 31, 42, 23, 38, 17, 18,…

Concept

For a set of raw (ungrouped) data values, the Mean is the sum of all values divided by the number of values, and the Range is the difference between the maximum and minimum value in the data set: Range = Maximum value − Minimum value.

Application

1. Sum the 12 marks: 36 + 37 + 31 + 42 + 23 + 38 + 17 + 18 + 35 + 25 + 29 + 35 = 366.

2. Divide the sum by the number of values to get the mean: Mean = 366 / 12 = 30.5.

3. Identify the maximum (42) and minimum (17) marks and subtract to get the range: Range = 42 − 17 = 25.

4. Subtract the range from the mean to get the required difference: Mean − Range = 30.5 − 25 = 5.5.

Cross-check

Sorting the data (17, 18, 23, 25, 29, 31, 35, 35, 36, 37, 38, 42) confirms the minimum is 17 and the maximum is 42, so the range of 25 is correct. Re-adding the values in pairs — (36+37), (31+42), (23+38), (17+18), (35+25), (29+35) = 73, 73, 61, 35, 60, 64 — gives a total of 366, confirming the sum and mean independently.