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NZAMT NZQA NZ Grapher NZ Maths Census at School Study It Khan Academy Desmos

Sample Variability & Sample Size

Inference HOME | Achievement Objectives | Overview | Statistical Cycle
- Write an introduction | Using NZgrapher | Discussing sample statistics
- Box plots | Discussing the boxplot & dotplot | Sampling methods | Sample variability and size
- Informal confidence interval | Comparing two populations - discussion
- Writing a report | Revision

8

Sampling & Sample variability

Review of calculate Sample Statistics & making Box plots

Sample Variability - how each sample varies from other samples (but is similar)

iNZight VIT on sampling demonstration

Sampling error notes (link to mathstatsfacilitators website)

To Achieve you MUST discuss sample variability, including the variability of the population estimates.

An understanding relating to sampling variability and variability of estimates must be evident. Another sample will give different medians and informal confidence intervals.

Video Chris Wilds overview of sample variation, bootstrapping & randomisation

Add in iNZight VIT on sample variation

Qualifications & Work Data Cards:
Data set csv
Variables | sets of axis
population boxplots & dot plots
One data card | All data cards
| excel version |

 

9

Sample Size

Activity: take sample from a population (data cards) manipulate, make box plots, compare with rest of class, increase sample size

The effect of Sample size: on sample variability, box plots and representation of the population

Samples of size n = 11
compared with n= 31

What sample size is most apppropriate?

Increasing the sample size increases the cost of the survey. As long as the sampling method is sound there is very little benefit in increasing the sample size above 35. We would get little extra useful information.

  • Note less variability in the medians: increasing sample size improves estimate. Draw in the interval for the sample medians.

  • Note less variability in the inter-quartile range

  • Note that estimates vary, even with larger sample size, and that it would be better to provide a range of possible values for the parameter, based on our estimate, rather than stating one value.

Class notes, Blank notes

Video Chris Wilds overview of sample variation, bootstrapping & randomisation

Links to Census at school Animations page
Sample size n = 10 animation
Sample size n = 100 animation
Sample size n = 1000 animation

 

 

Key Concepts
Taking a sample
Calculate Sample Statistics
Box plots
Sample Variability

A population has (usually) unknown
parameters: mean and median

Take a sample eg size n = 9

The sampling process should ensure the sample represents the population
A biased or poor sample will give poor population estimates

Calculate sample statistics

Make a box plot

Compare your box plot with other samples

What might the population median be?

We could use out sample median as an estimate, but we have a problem…


Sample:

About Box plots (Murdoch university)

Max =

Upper Quartile =

Median =

Lower Quartile =

Minimum =

 
"An investigator only gets to see one frame of the movie"

 

 

"An investigator only gets to see one frame of the movie"

What happens if we change the sample size?

A Sample size n = 15

A Sample size n = 60

Links to Census at school Animations page

Sample size n = 10 animation

 

Sample size n = 100 animation

 

Sample size n = 1000 animation

 

 

 

 

More animations like this at Census at school Animations page

 
 

 

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