Certificates / Quantitative aptitude / Average
Average: lesson, then the certificate test
Step 1: the lesson (about 1 min)
Average = sum of the values ÷ how many values. Most questions are solved through the SUM.
- Sum = average × count.
- A value that joins or leaves changes the sum: compare the new sum with the old one.
- If every value goes up by k, the average goes up by k.
Worked example
The average of 5 numbers is 20. A sixth number makes the average 22. What is the sixth number?
- Old sum = 5 × 20 = 100
- New sum = 6 × 22 = 132
- Sixth number = 132 − 100 = 32
Answer: 32
Watch out
- The average speed over two equal distances is 2xy ÷ (x + y), not (x + y) ÷ 2.
Made by Shishya (AI-assisted): a general method in our own words, with our own example; no exam or platform question is copied.
Step 2: the test
- 15 questions from Shishya's checked question bank, 20 minutes. Pass mark: 11 correct.
- Scored on Shishya's server; the answers are not shown afterwards, so the test stays fair. Each attempt draws new questions.
- Free. Your first test needs no account; sign up free to take more. Your answers and score are not stored; if you pass, you choose the name to print (ages 13 and up).
- It is a Shishya completion certificate — not a university or government credential. The test is not supervised.