Measures of Spread

Which distribution has the smallest standard deviation?_____

Which distribution has the largest standard deviation?_______

I know that the graph with the smallest standard deviation typically has the smallest ________________.

Variance =

Standard Deviation =

What are these math symbols?

Variance = =______________

Standard Deviation = =____________

Let's do one by hand!

Your Turn to find the Standard Deviation.

What's Step 1?____________ Do it.

What's Step 2?_______________ Do it.

What's step 3?____________ Do it

What's step 4?___________ Do it.

Compare your last two standard deviations. Which Standard Deviation is bigger? Circle the graph with the larger standard deviation.

A graph with the larger range typically has the larger standard deviation. However, these two graphs have the same standard deviation. How can you tell which standard deviation is larger if the graphs have the same range?_____________________________________________

Whew! Do you have to do ALL of that every time you need to know the standard

deviation??

NOPE!

(Stat, Edit)

Use your calculator to find the mean, variance, and standard deviation

mean = ______variance=_____standard deviation=_____

What if there are outliers?

The mean and standard deviation are not resistant to outliers. Outliers will pull the mean away from the center and make the standard deviation too large. If there are outliers, the median is a better measure of center and the IQR....interquartile range....is a better measure of spread.

Data A: 1, 2, 3, 4, 5 Data set B: 1, 2, 3, 4,500mean:________ mean:________stand. dev.______ stand.dev.______median:_____ median:_____IQR (Q3-Q1):______ IQR:_____range:_________ range:_______

Which statistics are affected by outliers?_________________________________________Which statistics are not affected by outliers?___________________________

For each boxplot, find the range and IQR. Which picture has the smallest IQR? Which has the largest IQR? Repeat for the histograms. Is it easier to see the IQR in boxplots or histograms?

Range:_________IQR:_________

Range:_________IQR:_________

Range:_________IQR:_________

Range:_________IQR:_________

Range:_________IQR:_________

Range:_________IQR:_________

Outlier... remember this?

outliers<Q1-1.5(IQR)outliers>Q3+1.5(IQR)

Write down the data values in the histogram. _______________________

What is the 5 number summarymin____ Q1=____ median=____ Q3 =____ max =_____

What is the IQR?______

Calculate Q1-1.5IQR=_____ and Q3 + 1.5IQR=____ Which values are outliers?____

Using the same distribution. Use your calculator to compute the standard deviation with the outlier(s) and without the outlier(s).

Standard deviation of all points:______

Standard deviation without outliers:_____

How has the standard deviation changed?_______________________________

Given the following data set, use your calculator to find the following summary statistics:

Multiply all of the data values by 2. Find the new summary statistics. How do the summary statistics change?

Linear Transformations on summary statistics

Compare the two data sets. Which summary statistics changed?___________________By how much?______________

Given the following data set, use your calculator to find the following summary statistics:

Add 5 to all of the data values. Find the new summary statistics. How do the summary statistics change?

Compare the two data sets. Which summary statistics changed?___________________By how much?______________

Summary of Linear Transformations:

Multiplying all numbers in the data set by a number causes_________________________________________ to change by a factor of _____________.

Adding a value to all numbers in the data set causes _____________ to change by ____________. ______________ will not change because _____________________.

Putting it all together...compare 2 distributions with center, shape and spread

3) Calculate the mean and standard deviation of Bryce's grade.

4) Calculate the mean and standard deviation of Brianna's grade.

5) Would you change your recommendation of who should get the award after computing the mean and standard deviation?