Alpha United
Can you find the mode and median number of goals scored by Alpha United?
Age
11 to 14
Challenge level
Problem
Alpha United have played fifteen games in their league.
The bar chart and pie chart show how many goals they scored in each of their matches.
Can you find the mode and median number of goals scored by Alpha United?
Image
Image
Getting Started
Student Solutions
The mode is the most common number of goals scored per match.
On the bar chart, this will be the tallest bar:
Image
Mode number of goals = 3
The mode is the most common number of goals scored per match.
On the pie chart, this will be the 'fattest' wedge:
Image
Mode number of goals = 3
The median is the middle value, when the data are in order.
The pie charts begin from 0 goals, and the number of goals increases in an anticlockwise direction, so the pie charts show the data in order.
After 180$^\circ$, the middle value is reached, so the wedge that the 180$^\circ$ line lands in is the median.
Image
Median number of goals = 2
Working out the median from the bar charts
The median is the middle value, when the data is in order. Alpha United played 15 matches, so the middle match is the 8th-lowest-scoring match (which is also the 8th-highest-scoring match), since 7 + 1 + 7 = 15.
So to find the median, we need to find the 8th lowest-scoring match on the bar chart.
Image
They scored 1 goal per match in 3 matches, so those are matches 4, 5 and 6.
They scored 2 goals per match in 2 matches, so those are matches 7 and 8.
So they scored 2 goals in their 8th-lowest-scoring match, so the median is 2.
We can check this, because they scored 3 goals per match in 5 matches and 4 goals per match in 2 matches. 5 + 2 = 7. So they scored more than 2 goals in 7 matches, so the 8th-lowest-scoring match is also the 8th-highest-scoring match.