Lemonade-Ed - Special Daisies (Activity)

Activity: Special Daisies

Not many left?

Students Joan and Lydia think they have found a rare variety of daisy growing among the ordinary daisies in a field that is to be dug up. The daisy has a bright pink tinge to its petals and grows well in moist conditions. Look at the map of the field.

On the map, 1mm represents 1m of the field. There are 1000mm in a metre, so 1mm on the map means 1000mm in the field. We call this a ratio of 1:1000. Any measurements on the map need to be multiplied by 1000 to give the real distance in the field.

Questions

Measure the distance from the gate to the middle of the largest oak tree on the map.
Work out the real distance in metres from the gate to the oak tree.

The Northfield Conservation Group wants to find out how many of the daisy plants are in the field. The evidence from their work might save the area from the developers.

Sampling

Joan thought they could count all the rare daisy plants in the field. Lydia suggested that instead of this they should look at a few small areas of the field as samples. 'We could find an area with lots of the daisies, and do our samples there,' she said. 'But that wouldn't be fair,' said Joan. 'It won't tell us the total number in the field.'

They decided that the fairest way of finding out how many of the daisies there are in the field without counting them all was to do random samples. This means doing samples in different places without choosing the places deliberately.

Question

Why do you think they decided not to count every single rare daisy plant in the field?

Joan and Lydia used a quadrat to do their sampling. Look at the above photo. This is a wooden frame measuring 1m on all four sides. This means it has an area of 1 m? (one square metre).

Joan threw a quadrat over her shoulder without looking where it would land. Then she looked at the ground inside the quadrat and counted the number of the daisy plants inside. She threw the quadrat and counted the daisy plants 10 times.

Question

How did Joan make sure her quadrats were placed randomly?
How big an area of field did Joan study? (How big was her sample?)

Joan's results

Joan and Lydia found 9 rare daisy plants in Joan's sample.

The whole sample had an area of 10m?. The field covers 4000 m2 in total. So the ratio of the area they sampled to the whole field is 1:400.

The ratio of the number of plants in the sample to the number of plants in the field is the same, 1:400. So to find the number of plants in the whole field, they multiplied the number in the sample by 400.

Question

How many plants did they think might be in the field?
Will this be the exact number of plants in the field?

A bigger sample

Lydia was still worried that most of the quadrats might have landed in parts of the field where there were not many of the daisy plants. This would mean their number for the total rare daisy plants in the field would be lower than the real number. She insisted that they do some more throws to get a more accurate result. So they did 20 new throws,

10 each. Here are the results:

Questions

How many rare daisy plants did Joan and Lydia find in these 20 new throws?
What is the ratio of the area of the new sample to the area of the whole field?
How many plants might there be in the whole field based on the new sample?