The class followed the outline closely. The document camera was not working today; someone said there was a power outage last night, which may have affected it. This just meant I had to write things on the board but it didn't really affect the lesson at all.
Below is the outline with some annotations enclosed within square brackets and italicized, [like this].
·
Mean-Median-Mode
o
Have everyone write down height to nearest inch
on a sticky note
o
On reverse side, have students write down what
they think the average height of the class will be.
o
Have students line up from shortest to tallest
o
Allow students to revise their estimate of the
class average now that they see what the heights look like
§
Convey the idea that in statistics, we
hypothesize about a variables value, we gather information and use this data to
make revisions to our hypothesis
o
Have one student from each end leave line and
place sticky note in appropriate bin on board
o
Continue until only one or two students left
o
What do remaining student(s) represent—the median!
o
Look at histogram on board
§
Describe the shape of this graph
§
Where is the mode?
o
Will the mean be larger, smaller or about the
same value as the median? [Held this discussion until later.]
o
Calculate the mean [Introduced sigma notation and x-bar. Discussed what the meaning of the mean is. Interestingly, most students knew how to calculate a mean but didn't understand what it represented other than a vague notion of the center. They could not articulate how what this measurement of center represented. It was a good discussion. I didn't have manipulatives but was able to create a mental image of each student holding small disks totaling their height in inches. The task would be to share out the disks until everyone had the exact same number of disks in hand. Taller individuals would be giving up disks and shorter individuals would be taking disks. Eventually, everyone would have the same whole number and a sub-group would possess one extra, the fractional part of the mean value.]
§
How did your personal estimate compare to the
actual mean? [Didn't discuss this since I decided to use this as a way to promote the underlying statistical process of estimate, analyze, and revise estimate.]
o
Show graph shapes and ask where mean vs median
will lie [First discussed the comparison of median and mean with height data before discussing comparisons. Wrote out the relationships between mean and median underneath graph.]
·
Variation
o
How would you describe the spread of the height
data distribution?
o
Range
§
difference between smallest and largest values
§
what are limitations using the range
o
How else might we look at spread?
§
Discuss ideas, focus on those looking at how far
away from mean, lead discussion this way if needed
o
What if we take average difference from the
mean? [Introduced the term "deviation from the mean" here.]
o
What can we do to account for negative and
positive differences cancelling each other out. [One student suggested absolute values--perfect!]
o
Absolute values work but are not computationally
convenient, what is another way to manipulate values to eliminate negative
values?
§
Remind about distance formula and squaring [No reminder needed. One student suggested multiplying values and all I had to do was ask the class what we could multiply by.]
o
Let’s take squared differences from the mean and
average these
o
Put up four values, say 2, 5, 8, and 9. The mean
is 6. If you know there are four values with a mean of 6 and you know three of
the values (2, 5, and 8) you can find the fourth value. So, when calculating
the mean difference from the sample mean, need to divide by n-1 to account for
this fact. [I actually just used the values 1, 2, 3, and 4 here.]
o
We started with inches but the mean squared
deviations are in squared inches. How do we get back to our original units? [Students said we'd need to take the square root.]
o
Let’s try it on a smaller data set first. Here
are two data sets to work with. [At this point I showed students how to use their calculators to calculate these values.]
o
What do the standard deviations tell you about
these two data sets?
§
Discuss [Discussion focused on what does the standard deviations tell you about the data sets. To help give additional practice, I asked students to use 10 data values such that the mean would equal 40. For one data set I required that the standard deviation equal 5 (within 0.2) and for a second data set I required that the standard deviation equal 15 (within 0.2). This homework gives students an opportunity to get comfortable working with the formulas and also gaining a better sense of what the standard deviation represents.]
§
Show dot plots of the data [Did not show since document camera was not functioning.]
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