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 CensusAtSchool Australia

CaSQ 29 - Comparing samples to a population using Excel

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 How to: Get a Random Sample from CensusAtSchool Go to the CensusAtSchool Random Sampler to download a sample. Reference year: (Select year) Sample size: At least 200 students Select questions: Environmental issues Location: Select location Year level: (Select a range of year levels) To protect privacy there is a rule built into the sampler that the requested sample size cannot exceed 10% of the respondents for the parameters entered.

A sample is often used to infer information about a population when it is impractical to collect data on the whole population. It is important that the sample does not exhibit bias. The usual way to overcome the possibility of bias is to select a simple random sample (SRS).

However, the size of the sample is also important. Imagine we wanted to find the mean height of all two hundred Year 10 students at a school. If we took a sample size of one this is too small as this person may be much shorter than most. On the other hand, a sample size of 199 is too big – we may as well question all Year 10s.
In this investigation you are to collect data for different sample sizes and note any pattern.

From your random sample select the question related to Environmental Issues - reducing pollution, recycling rubbish, conserving water, forests and the marine environment.

Student responses on various environmental issues were recorded as numbers from 0 – 1000 where 0 represented minimal importance and 1000 represented maximum importance.

1. Select one of the environmental issues you want to investigate. Copy the data as a list in Excel.

2. Set up a table for your issue like the one below an give it a heading.

 sample size mean student opinion on water 10 20 30 40 50 60 80 100 150 200

3. Calculate the mean numerical value for your issue for all 200 students in your sample. Do this by selecting your data and in the cell in the table next to 200 enter
= AVERAGE(a1:a200) where a1 is the first cell and a200 is the last cell

4. Next, follow the same steps to calculate and enter the mean for the other sample sizes shown in the table.

5. Select the data in your table and make a scatter plot.

6. If 200 is the full population, comment on how the mean of the different sample sizes compares with the mean of the whole population as the sample size increases.