P11 | Maths Made Easy

P11

Question: Gracie grows 40 sunflowers one year and records their heights in a frequency table. Find the modal group and the group containing the median. 

Solution: The modal group is whichever group has the most things – in this case sunflowers – in it. Looking at the table, we see that 170 < w \leq 180 is the modal group.

For the median, we want to work out which group the middle term is in. There are 40 sunflowers, so the median will be the 20th one. Normally looking for the median we have to write the terms in size order, but the table already does that for us.

Up to 170cm, there are 5+9=14 sunflowers. Up to 180cm, there are 14+15=29 sunflowers. That means that the 170 < w \leq 180 category contains the 15th to the 29th sunflower, when put in order, meaning the 20th in somewhere in there.

Therefore, 170 < w \leq 180 group contains the median.