Mode and median from a table
When there are a large number of values present, the data may be presented in a table.
The pupils in year 6 at St Jude’s School were asked how many siblings they had. The results are displayed in the table.
The mode number of siblings is the group that contains the highest frequency.
For pupils in year 6, the mode number of siblings is 2.
To find the median, we first need to work out what position in the data the median will be. If there are n pieces of data, the median value will be in position \(\frac {n~+~1} {2}\).
As there are 50 people, the median value will be the 25.5th value, which makes it between the 25th and 26th value.
The first 7 people have 0 siblings, 20 people have 0 or 1 sibling, which means the 25th and 26th value are in the group showing 2 siblings, so this is the median.
When there are a lot of categories, data is often put into groups.
Groups may be written as:
0 – 4 meaning it contains the numbers 0, 1, 2, 3 and 4.
\({0}~\leq~\times~\textless~{10}\) meaning all values between 0 and 10 (not including 10)
Data values that can take any value (not constrained to certain specific values), eg length of foot, body mass of newborn babies. data will be presented in this way because it can take any number of values.
The grouped frequency table shows the distances thrown in a javelin competition.
Question
What is the modal group?
The modal group is \({20}~\leq~\times~\textless~{40}\)
This is the group with the highest frequency.
Question
Which group does the median lie in?
The median is in the group \({20}~\leq~\times~\textless~{40}\)
There are 29 pieces of data; \(\frac {29~+~1} {2}~=~{15}\), so the median is the 15th value.
The first 9 pieces of data are in \({0}~\leq~\times~\textless~{20}\), so the 10th – 19th pieces of data are in \({20}~\leq~\times~\textless~{40}\)
