MDM4U Measures of Spread; Sampling

Yesterday

We learned about measures of spread (sorry I forgot to post this!). The big one is Standard Deviation, which is represented by the greek letter for a population and for a sample. There is a formula, but it’s long and not really important here. It’s in your textbook.

We worked on the Chromebooks to find the mean and standard deviation for a given data set.

Here’s a video that explains why we have standard deviation and how it works:

Today

We talked a bunch about sampling and how to make good questions. We didn’t finish our questions chat, so that’ll be what we do on Monday morning. Here’s the promised page about sampling and sample types:

sampling

Have a great weekend!

MDM4U Normal distribution and Z-scores; tomorrow’s work too 2016-05-11

We started to talk about the normal distribution today. This is a continuous distribution defined by two values: the mean and the standard deviation.

We learned about how to calculate z-scores for specific data values. Tomorrow we’re going to practice that skill, and we’re going to extend it further to solve problems.

Want a preview? Here’s what we did today along with tomorrow’s learning. Let me know if you see any boo-boos in my work.

Quartiles, Percentiles, and Z-Scores

I’ll post tomorrow’s practice work after class.

MDM4U Measures of Spread; Gizmos 2016-05-09

We learned about standard deviation today! It’s a way to measure how spread out your data is.

For example, if you have a data set with a mean of 10, a mode of 10, and a median of 10, you don’t know a lot about the values. You know a lot about the middle, but not the edges.

Standard deviation is a measure of how spread out the values are. Variance is another measure that we don’t use much in this course (it’s the square of standard deviation). We’ll learn more about how to use and interpret the standard deviation, so that’s enough to go on for now.

For notation, we use different symbols for mean, standard deviation, and variance depending on whether we’re talking about a population or just a sample.

Population	Measure	Sample
	mean
	standard deviation
	variance

We also used two Gizmos! from explorelearning.com: the Real-Time Histogram and the Sight vs. Sound Reactions. If you weren’t here, ask me tomorrow for the class enrollment code (I can’t post it here).

Also, see if you can beat my score for Sight Reaction (that is, have a lower mean and/or a lower standard deviation):

MDM4U Measures of Spread: Standard Deviation – 2015-12-08

We briefly reviewed the measures of central tendency that you’ve known for years (mean, median, mode) and then talked at length about how to describe how “spread out” values are.

We noted that two distributions of values could have very different shapes (remember the tall-skinny vs. short-wide graphs, and the two-bump camel graphs) but have the same mean, median and mode. In short, those aren’t always helpful in describing our data sets.

What we want to be able to do is describe how spread out our data is. Another way to think about it: if you choose an individual at random from your population, how likely are they to be far from the mean? If you’re data is spread out, they’re more likely to be far from the mean.

This is what standard deviation is for: it lets us describe the spread in a numerical way.

If you were away, or if you want a nice review of these ideas, check out this link:

http://www.mathsisfun.com/data/standard-deviation.html

This is a nice, clear explanation of standard deviation including pictures of dogs. If you have a friend with a Dachshund, you might want to show her too.