1. Ch. 4 – Displaying Quantitative Data (Day 1)
Part I – Exploring and Understanding Data
Ch. 4 – Displaying Quantitative Data (Day 1)

2. Here are the record high temperatures for each of the 50 states
Here are the record high temperatures for each of the 50 states. What can we learn about temperature in the U.S. from this data?

3. Make a Picture
Remember your first rule of data analysis – Make a Picture!
Can we use a bar graph or a pie chart?
No! These are quantitative data, not categorical, so we need a new kind of graph

4. Histograms A histogram looks similar to a bar graph
First, we have to divide our data into piles of equal width, called bins or classes
Then we count the number of values that fall into each bin, and those numbers make up the heights of the bars
We have some freedom in deciding how wide our bins are – this can change the look of the histogram

5. So let’s try it…
Before we divide up our data into bins, we should first figure out the range of the data (largest value – smallest value)
In this set of data, the range is ____________
Now we can decide how many bins we want, based on a width that would be easy to draw
Normally we want somewhere between 5 and 20 bins in our graph

6. Choosing the number of bins
Too few
Too many
Just Right
This is subjective, and depends on the data set.

7. For this data set…
Since we have a range of 34 degrees, bins with a width of 5 degrees would give us 7 bars, which is a good starting place to try
You can start your first bin with your lowest number, or a number that makes sense and is near that value
In this problem, we’ll start with our lowest number: 100 degrees

8. Putting the values in bins
We know we want our graph to look like this:
We just need to figure out how many values fall in each bin
Temperature
Frequency (# of states)

9. Putting the values in bins
Placing our data in bins should be easy – if a state had a high temperature of 102 degrees, this would fall in the first bin, since it’s between 100 and 105
The only problem we have is what to do with the numbers on the border between two bins
The standard way to do this is to put numbers on the border into the next highest bin
For example, a record temperature of 105 degrees would go into the second bin

10. Putting the values in bins
Tally the number of values for each bin…
100 – 104 (really …):
105 – 109:
110 – 114:
115 – 119:
120 – 124:
125 – 129:
130 – 134:

11. Now draw the graph…
Temperature
Frequency (# of states)
This is a picture of the distribution of U.S. record high temperatures.

12. Using your calculator Use the STAT menu Enter the data into a list
These lists can be sorted (ascending or descending), used for graphs & other calculations, copied, and manipulated with mathematical operators

13. Using your calculator Use the STAT PLOT menu (above Y=)
Choose a histogram and the list to use
Leave the frequency at 1

14. Using your calculator
ZOOM #9 (ZoomStat) for your calculator to set the bin widths automatically

15. Using your calculator
If you want to set the widths yourself, adjust the XScl in the Window menu

16. Using your calculator
Hit “Trace” to see the boundaries and heights of the bars
Remember – your graph still needs labels and scale, just like when you create it by hand!

17. Homework 4-1 For the following problems, make a histogram
You may create the histogram on your calculator and then sketch the histogram onto your hw paper.
Remember to label when you transfer your histograms to your hw.
Pg. 72 # 42, 49, 50