Random Sampling KEY
Scientists cannot possibly count every organism in a population. One way to estimate the size of a population is to collect data by taking random samples. In this activity, you will look at how data obtained from random sampling compare with data obtained by an actual count.
Teacher Note: Students often get confused about the sampling part. You may need to model the act of choosing the slips of paper and explain it is simply a way to pick a plot at random.
Procedure:
1. Tear a sheet of paper into 20 slips, each approximately 4cm x 4 cm.
2. Number 10 of the slips from 1 to 10 and put them in a small container.
3. Label the remaining 10 slips from A through J and put them in a second
container.
The grid shown below represents a meadow measuring 10 m on each side. Each grid segment is 1m x 1m. Each black circle represents one sunflower plant.
4. Randomly remove one slip from each container. Write down the number-letter
combination and find the grid segment that matches the combination. Count
the number of sunflower plants in that grid segment. Record this number on
the data table. Return each slip to its appropriate container.
5. Repeat step 5 until you have data for 10 different grid segments (and
the table is filled out). These 10 grid segments represent a sample. Gathering
data from a randomly selected sample of a larger area is called sampling.
6. Find the total number of sunflower plants for the 10 segment sample. This
is an estimation based on a formula. Add all the grid segment sunflowers together
and divide by ten to get an AVERAGE number of sunflower plants per grid segment.
Record this number in the table. Multiple the average number of sunflower
plants by 100 (this is the total number of grid segments) to find the total
number of plants in the meadow based on your sample. Record this number in
your data table.
7. Now count all the sunflower plants actually shown in the meadow. Record
this number in the data table. Divide this figure by 100 to calculate the
average number of sunflower plants per each grid.
Random Sampling Data |
Actual Data |
||
| Grid Sigment (number - letter) |
Number of Sunflowers | Students need to count these out, or you can write on board Total number of Sunflowers _230__ Average number of Sunflowers
|
|
| answers vary, but most of the grids have 3 | |||
| Total Number of Sunflowers | ~ 20 | ||
| Average (divide total by 10) | ~2 | ||
| Total number of plants in meadow (multiply average by 100) |
~200 | ||
Analysis:
1. Compare the total number you got for sunflowers from the SAMPLING to the ACTUAL count. How close are they?
the numbers should be fairly close
2. Why was the paper-slip method used to select the grid segments? this randomizes which plots are counted
3a. A lazy ecologist collects data from the same field, but he stops just on the side of the road and just counts the 10 segments near the road. These 10 segments are located at J 1-10. When he submits his report, how many sunflowers will he estimate are in the field?
For his section, there are 7 sunflowers per 10. That's an average of .7 per grid. .7 x100 = 70 flowers
b. Suggest a number why his estimation differs from your estimation. He estimated an area that had fewer flowers, possibly because of the nearness to the road. Had he counted in the center of the field, the numbers would be closer.
4. Population Sampling is usually more effective when the population has an even dispersion pattern. Clumped dispersion patterns are the least effective. Explain why this would be the case.
If sunflowers were all clumped in the center of the meadow, then slips randomly drawn from outside plots would suggest there were less flowers. Even dispersion means that each plot has about the same number
5. Describe how you would use Sampling to determine the population of dandelions in your yard. make a grid in your yard and
randomly select different areas to count the dandelions, average the numbers and then multiply by the number of plots your grid contains.
6. In a forest that measures 5 miles by 5 miles, a sample was taken to count the number of silver maple trees in the forest. The number of trees counted in the grid is shown below. The grids where the survey was taken were chosen randomly. Determine how many silver maple trees are in this forest using the random sampling technique. Show your work!
First average the data for each plot: 7+3+5+9+11 = 35 ................... 35/5 = 7 trees per grid
The number of plots is 25. 7 x 25 = 175 trees in the entire area
| 7 | ||||
| 3 | ||||
| 5 | ||||
| 11 | 9 | |||