# Standard Deviation

```Name: ______________________
Period: ____________
9/7/2018
Warm Up:
Use the stemplot from the problem below to calculate a five number summary
and identify if there are any outliers.
Here a stem plot of travel time to work for 20 randomly selected New Yorkers.
Earlier, we found that the median was 22.5 minutes.
1. Based only on the stemplot, would you expect
the mean travel time to be less than, about the
same, or larger than the median? Why?
2. Use your calculator to find the mean travel
3. Would the mean or the median be a more appropriate summary of the
center of this distribution of drive times?
Standard Deviation
______________________________________________________________
Variance
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Hair Measuring Activity -- What is Standard Deviation?
1. Have students record the hair length on the board and then in the table
below. So, the variable of interest, x, is hair length.
xi
2. What is the average hair length in the class, based on this very
“unrandom” sample?_________ This is called x .
3. What is the average distance of hair length away from this mean? To
calculate this, subtract the mean form each of the hair lengths (xi). Now
add these distances and divide by n (the number of hair lengths
recorded). Hmmm.
4. What happened???
5. How can we adjust what we did before? What can we do?
6. Because this standard deviation is based on a sample (we’re pretending
for the moment that we actually took a random sample), it is not an
accurate estimate of the true population standard deviation. To make
this value an unbiased estimate, we divided by n – 1 instead of n.
What we’ve done is develop the formula for the standard deviation. You do
not have to memorize it, but you do need to be able to reproduce it (given the
formula) and to understand it.
Follow- up to hair length and standard deviation.
1.)
2.)
3.)
4.)
5.)
6.)
7.)
List the hair length of each member of your group.
Find the average hair length of your group.
Find the difference from the mean for each person in your group.
Square this difference for each person in your group.
Take the average of these squared differences.
Take the square root of the average of the sum of the squared differences.
What did you find? Rhymes with “Lanyard Re-creation”

What conclusion(s) can you arrive at if the standard deviation for the hair
length of an entire class is zero?

One student answered that the class is bald. Are they correct? Are they correct
for the right reason? Is having a bald class the only way the standard deviation
can be zero?

Consider the groups in the room and identify the group with the smallest
standard deviation. The largest.

A new girl was added to the class and her hair length was the equal to the
average hair length for the class. What impact will this addition have to the
standard deviation for the class? To the mean? Don’t answer this one too
quickly…

If everyone cut an inch off of their hair, what would happen to the standard
deviation for the class? To the mean?

If everyone ate a ton of bananas and their hair length doubled, what would
happen to the standard deviation for the class? To the mean?

In order for the standard deviation to remain the same what type of hair
length(s) of student(s) need to be added to the class?
Here are the foot lengths (in centimeters) for a random sample of 7 fourteen-year-olds
from the United Kingdom.
 25, 22, 20, 25, 24, 24, 28
 Find the “average” squared deviation and the standard deviation.
```