# Sampling and Normal Distribution

###### Description

This interactive simulation allows students to graph and analyze sample distributions taken from a normally distributed population.

The normal distribution, sometimes called the bell curve, is a common probability distribution in the natural world. Scientists typically assume that a series of measurements taken from a population will be normally distributed when the sample size is large enough. In this Click & Learn, students can easily graph and explore the distributions of different samples taken from an idealized normally distributed population. Students can set the sample size, population mean, and population standard deviation, and observe how the sample distribution shifts when changing any of these variables.

The accompanying worksheet guides students’ exploration.

The “Resource Google Folder” link directs to a Google Drive folder of resource documents in the Google Docs format. Not all downloadable documents for the resource may be available in this format. The Google Drive folder is set as “View Only”; to save a copy of a document in this folder to your Google Drive, open that document, then select File → “Make a copy.” These documents can be copied, modified, and distributed online following the Terms of Use listed in the “Details” section below, including crediting BioInteractive.

###### Student Learning Targets

- Explain that standard deviation is a measure of the variation of the spread of the data around the mean.
- Explain that larger sample sizes are desirable when collecting data about a population, because they are more likely to reflect the true distribution of the population.
- Calculate the standard error of the mean (SEM) and explain that it measures how much the mean of a sample reflects the mean of the population from which the sample was drawn.
- Use SEM to calculate 95% confidence intervals (CIs), represent the Cls on a graph as error bars, and compare error bars to determine if there is a difference among the populations from which the samples came.

##### Details

average, confidence interval (CI), error bar, Gaussian distribution, histogram, measurement, population, random sample, standard deviation, standard error of the mean (SEM)

The resource is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International license. No rights are granted to use HHMI’s or BioInteractive’s names or logos independent from this Resource or in any derivative works.

##### Curriculum Connections

HS-LS2-1; SEP2, SEP5

SP1, SP2, SP3, SP4, SP5

C.1

III.A

2.1

Common Core (2010) ELA.RST.9-12.7, ELA.WHST.9-12.1

Math.A-REI.6, Math.N-Q.1, Math.F-IF.7, Math.S-ID.4, Math.S-ID.7; MP2, MP4

CC5; DP2, DP3