1.  Representing Data

2. Do Now 02/05  How can confidence intervals and levels help us with the reliability of our results and samples?

3. Paper Planes  At your desk, individually, build as many paper planes as you can in a span of 4 minutes.  They should be able to fly. They can be as large or as small as you want them to be!  Keep track of how many you make independently and place your name on the board when you have counted and place the total next to your name.

4. Think  Now that you have the class data on how many paper planes each person built, how would you graph this data? Work with your partner sitting next to you. Describe what it looks like when you’re done. Be able to justify:  Why you chose to graph your data in a specific graphing template  What does this data show us?  What does it look like?  Make sure you have a graphing representation

5. Today we will…  3.3: accurately describe various distribution types/shapes and justify why data might have a particular distribution  3.5: accurately graph data in a histogram and explain any potential patterns/trends I see

6. Histograms  We are going to revisit histograms, because this is the graph that you use to graph and represent continuous data.  In our case, our continuous data—data with a range—was to see how many paper airplanes we could make as a class per person.  There are minimums (0  1) and maximums (maybe some people made 19  20 in that time).

7. Histograms  Either way, we want to measure the frequency—or how many people/times—certain data showed up in a specific bin or range of values.  First thing first, we need to order our data in ascending order (low to high)  2. we need to find the range of our values (highest value-1)  3. we need to establish our bins  small ranges that values will fall in (it can be 1-10, or every 5 digits, or 2 etc.)  4. we note the frequency—how many times values fall within our bins—on the y-axis

8. Histograms  Let’s look at our class data and:  1. arrange the list of values in order  2. find our range  3. make bins (mini-ranges) within our data. How do you want to break it up?  4. measure the frequency of data within each bin

9. Histograms  Now, lets look at our data  What does our graph look like? Look at the shape. Remember our discussion on normal distributions.  What do you think the mean (average) is just by looking at the graph?

10. Shapes of our Distribution

11. Symmetric  Symmetric and UNImodal: this distribution has ONE PEAK and is even on both ends. Consider this an ideal distribution when comparing to the bell- shaped curve.

12. Skewed—off center  Skewed Right: this means we have more values in the lower ends than we do the right ends of our graph. The tails pointing to the right are lower in frequency. This can be caused by outliers present in the data (extreme values)  Skewed Left: the tips of the tails in the left side of the graph are lower in frequency. We have more values on the higher end of the scale.  Ex.: more people in class are taller than there are short people. Can also be caused by outliers in the data (extreme values) that pull the data towards the

13. Shapes of our Distribution

14. Check-in Practice  From the data set below: find the range, establish your bins, and find the frequency of values within each bin, then draw your histogram  Scores on an exam:  40,50, 65, 65, 75, 80, 90, 95, 20, 55, 75, 78, 79, 82, 62, 79, 72, 70, 98, 45, 37, 29, 45, 89, 92, 81  Describe your data shape. What does it look like?

15. Exit Slip  Draw a histogram for the following scores out of 100 points.  80, 40, 45, 50, 62, 76, 78, 91, 34, 74, 72, 66, 87, 49, 56, 59, 52, 78, 91, 98, 55, 63, 18, 23, 35  Estimate what your average is. What is your range of values?

16. Shapes of our Distribution