Averages

Maths, Statistics. Usually met in years 7 to 10.

Find the mean, median and a missing value, including from a frequency table.

What you practise

Finishes with missing values and frequency tables. Practice moves up a level when a round goes well and down when it does not.

Each sample comes with the method and the reason every wrong option is wrong. Real practice rounds are ten questions at your level.

Sample question, level 2 of 5

Find the median of 17, 32, 34, 16, 37.

Show the answer and method

Answer: B, 32

The method: Put them in order: 16, 17, 32, 34, 37. The middle one (number 3) is 32.

Why the other options are wrong:

A, 34: The wrong position in the ordered list was used.
C, 30: Close, but check your working: this is a small slip away from the answer.
D, 27.2: This is the mean, not the median.
E, 21: This is the range, not the median.

Sample question, level 4 of 5

The mean of 5 numbers is 10. Four of the numbers are 16, 10, 3, 19. What is the fifth number?

Show the answer and method

Answer: E, 2

The method: The total of all 5 numbers is 5 × 10 = 50. The four known numbers add to 48, so the fifth is 50 − 48 = 2.

Why the other options are wrong:

A, 38: The mean was subtracted from the total of the four, not the total of all five.
B, 50: This is the total of all five numbers.
C, 10: The mean was given as the missing number.
D, 12: This is the mean of the four known numbers.