Measures of centre
Calculate the mean, median and mode of a data set, and find an unknown value given the mean.
Worked examples
Finding the mean
Straightforward
Problem
Find the mean of the data set .
1
Add all the values together.
2
Count the number of values.
There are 5 values in the data set.
3
Divide the sum by the number of values.
Answer
The mean is .
Finding the median and mode
Moderate
Problem
Find the median and mode of the data set .
1
Sort the data in ascending order.
2
Find the median (the middle value). There are 7 values, so the median is the 4th value.
The 4th value in the sorted list is . Median .
3
Find the mode (the value that appears most often).
The value appears 3 times, which is more than any other value. Mode .
Answer
Median , mode .
Finding an unknown value given the mean
Challenging
Problem
Five numbers have a mean of . Four of the numbers are . Find the fifth number.
1
Use the mean to find the total sum required.
2
Find the sum of the four known values.
3
Subtract to find the fifth number.
Answer
The fifth number is .
Practise
Q1·Straightforward
Find the mean of the data set .
Explanation
Add all the values: . There are 5 values, so the mean is .
Q2·Straightforward
The test scores of five students are . Find the mean score.
Explanation
Add the scores: . There are 5 scores, so the mean is .
Q3·Straightforward
Find the mean of the values .
Explanation
Add the values: . There are 4 values, so the mean is .
Q4·Straightforward
A student records the number of hours of homework done each day for six days: . Find the mean number of hours.
Explanation
Add the values: . There are 6 values, so the mean is .
Q5·Moderate
Find the median of the data set .
Explanation
Sort the data: . There are 5 values, so the median is the 3rd value: .
Q6·Moderate
Find the mode of the data set .
Explanation
Count the frequency of each value: appears 3 times, all others appear once. The mode is .
Q7·Moderate
Find the median of the data set .
Explanation
Sort the data: . There are 6 values (an even number), so the median is the mean of the 3rd and 4th values: .
Q8·Moderate
Find the mode of the data set .
Explanation
Count frequencies: appears 3 times, appears 2 times, and each appear once. The mode is .
Q9·Challenging
Five numbers have a mean of . Four of the numbers are . Find the fifth number.
Explanation
The total sum needed is . The sum of the four known values is . The fifth number is .
Q10·Challenging
The mean of four numbers is . Three of the numbers are . Find the fourth number.
Explanation
The total sum needed is . The sum of the three known values is . The fourth number is .
Q11·Challenging
Six numbers have a mean of . Five of them are . Find the sixth number.
Explanation
The total sum needed is . The sum of the five known values is . The sixth number is .
Q12·Challenging
Five numbers have a mean of . Four of them are . Find the fifth number.
Explanation
The total sum needed is . The sum of the four known values is . The fifth number is .