# 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.

###### 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

1.C.1, 4.B.4; SP1, SP2

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