Average

Read the formula sheet first, then work through the 10 questions below. Each answer comes with a step-by-step solution — read it even when you get the question right, the shortcut is often faster than your method.

Formula sheet

• Average = Sum of observations / Number of observations.
• Average of first n naturals = (n+1)/2; of first n evens = n+1; of first n odds = n.
• Adding a new item that raises avg by k: new item = old avg + k × (new count).
• Replacing item: new avg change × n = (new item − old item).
• Weighted average = Σ(nᵢ·aᵢ)/Σnᵢ.
• Average speed for equal distances = 2xy/(x+y); for equal times = (x+y)/2.
• Average of consecutive/AP terms = middle term = (first + last)/2.

Practice

Pick an answer to see whether it is right and the worked solution. Your score is saved when you finish the set.