Problem Solving: Averages & Range
1) Three numbers have a median of 7, a range of 7 and a
total of 16. Give the three numbers.
2) The mean of 4 numbers is 8. Three of the numbers are
2, 6 and 11. Give the fourth.
3) The median of 6 numbers is 10, the mode is 8, the range
is 8 and all numbers are even. Find the numbers.
4) Nine elephants have a mean average weight 2300kg. A
10th elephant weights 2500kg. Find the mean weight of all
10 elephants.
5) Out of 30 students the 13 boys had a mean average
score of 65% in their last science test. All 30 students in
the class had a mean average score of 72%. Find the mean
average of the girls. Give your answer to 2dp.
6) 7 prime numbers have a mean of 10. The median is 11,
the mode is 17, the IQR is 14 and the range is 15. Find all
7 numbers.
7) Five office workers have a mean average salary of
£18,000. Three more people join the company, the mean
average salary is now £20,000. Given the three new
workers have salaries in the ratio 3:5:6 find their salaries.
8) 30 people are asked to record how many hours sleep
they had last night (to the nearest whole no. of hours).
The results are given below. Given the mean was 8.4 hours
find the missing values.
Hours Sleep
7
8
9
10
Frequency
14
11
9) The table below gives information about the ages of
people in a badminton club. Using this information the
mean is estimated to be 43.625 find the missing value.
Age ‘a’ in years
20 ≤ a < 30
30 ≤ a < 40
40 ≤ a < 50
50 ≤ a < 60
60 ≤ a < 70
Frequency
17
23
9
16
Problem Solving: Averages & Range ANSWERS
1) Three numbers have a median of 7, a range of 7 and a
8) 30 people are asked to record how many hours sleep
they had last night (to the nearest whole no. of hours).
total of 16. Give the three numbers. 1, 7, 8
The results are given below. Given the mean was 8.4 hours
find the missing values.
2) The mean of 4 numbers is 8. Three of the numbers are
2, 6 and 11. Give the fourth. 13
3) The median of 6 numbers is 10, the mode is 8, the range
is 8 and all numbers are even. 8, 8, 8, 12, 14, 16
4) Nine elephants have a mean average weight 2300kg. A
10th elephant weights 2500kg. Find the mean weight of all
10 elephants. 2320 kg
5) Out of 30 students the 13 boys had a mean average
score of 65% in their last science test. All 30 students in
the class had a mean average score of 72%. Find the mean
average of the girls. Give your answer to 2dp. 77.35%
6) 7 prime numbers have a mean of 10. The median is 11,
the mode is 17, the IQR is 14 and the range is 15. Find all
7 numbers. 2, 3, 7, 11, 13, 17, 17
7) Five office workers have a mean average salary of
£18,000. Three more people join the company, the mean
average salary is now £20,000. Given the three new
workers have salaries in the ratio 3:5:6 find their salaries.
£15,000, £25,000 and £30,000
Hours Sleep
7
8
9
10
Frequency
3
14
11
2
9) The table below gives information about the ages of
people in a badminton club. Using this information the
mean is estimated to be 43.625 find the missing value.
Age ‘a’ in years
20 ≤ a < 30
30 ≤ a < 40
40 ≤ a < 50
50 ≤ a < 60
60 ≤ a < 70
Frequency
17
23
9
16
15