Arithmetic mean, median and mode
Answers are for parents and teachers.
1
Find the mean of 12, 15, 9 and 14.
Sum = 50 and 50 ÷ 4 = 12.5.
2
The mean of six numbers is 7. Five of them are 3, 5, 8, 9 and 6. Find the sixth.
Total = 6 × 7 = 42. Known sum = 31. The sixth number is 42 − 31 = 11.
3
Find the mean from the table: x = 1, 2, 3, 4 and f = 2, 5, 5, 3.
Σ f = 15 and Σ f·x = 2 + 10 + 15 + 12 = 39. Mean = 2.6.
4
x = 1, 2, 3 and f = 5, 3, k. The mean is 2. Find k.
Σ f·x = 5 + 6 + 3k = 11 + 3k and Σ f = 8 + k. 11 + 3k = 16 + 2k, so k = 5.
5
The data 2, 4, 5, 6, 8 get a new value 41. Find the mean and the median before and after.
Before: mean 25 ÷ 5 = 5, median 5. After: mean 66 ÷ 6 = 11, median (5 + 6) ÷ 2 = 5.5.