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

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? 112 110 107 116 120 100 118 112 108 113 127 117 114 110 120 120 116 115 121 117 134 118 118 113 105 118 122 117 120 110 105 114 118 119 118 110 114 122 111 112 109 105 106 104 114 112 109 110 111 114

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

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

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

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

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

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) 100 105 110 115 120 125 130 135

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

Putting the values in bins Tally the number of values for each bin… 100 – 104 (really 104.999…): 105 – 109: 110 – 114: 115 – 119: 120 – 124: 125 – 129: 130 – 134:

Now draw the graph… Temperature Frequency (# of states) 100 105 110 115 120 125 130 135 This is a picture of the distribution of U.S. record high temperatures.

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

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

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

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

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!

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