Histogram – a picture of a Grouped Frequency Distribution To accompany Hawkes lesson 2.2b (ii) Original content by D.R.S.

Inputs and Outputs Output – a Histogram Numerical data Input – Frequency Distribution Output – a Histogram Numerical data Not categorical data Grouped into classes Each class has a count, a frequency, how many data values fall within that low-to-high class. Horizontal axis has numerical class boundaries Vertical axis has frequency of classes. Height of each bar indicates the frequency of the each class 4/13/2019

Input: a frequency distribution The data set: the 5K runners’ finishing times. The data were grouped into a frequency distribution. Each class is a low-to-high range of temperatures. We have the right ingredients for a histogram: Frequency distribution (classes and counts) Numerical data (not categorical) 4/13/2019

Recall – we had constructed this frequency distribution earlier. Time (minutes) Frequency 20.0000-24.9999 9 25.0000-29.9999 26 30.0000-34.9999 23 35.0000-39.9999 14 40.0000-44.9999 7 45.0000-49.9999 11 50.0000-54.9999 10 55.0000-59.9999 60.0000-64.9999 2 65.0000-69.9999 1

Recall this distinction between “Class Limits” vs. “Class Boundaries” 20.0000-24.9999 19.99995 – 24.99995 25.0000-29.9999 24.99995 – 29.99995 30.0000-34.9999 29.99995 – 34.99995 Etc. 55.0000-59.9999 54.99995 – 59.99995 60.0000-64.9999 59.99995 – 64.99995 65.0000-69.9999 64.99995 – 69.99995

Input: This frequency distribution of runners’ times Time (minutes) Frequency 19.99995-24.99995 9 24.99995-29.99995 26 29.99995-34.99995 23 34.99995-39.99995 14 39.99995-44.99995 7 44.99995-49.99995 11 49.99995-54.99995 10 54.99995-59.99995 59.99995-64.99995 2 64.99995-69.99995 1 For a histogram, we use the CLASS BOUNDARIES, not the class limits!

Histogram

Horizontal Axis We used the Class Limits as our labeling on the horizontal axis. This would probably make the most sense to the readers. Time (in minutes)

Horizontal Axis But statistics books - and your assignments – want the axis labels to be the class boundaries.

Important Design Notes! The vertical axis begins at 0. Tickmarks are well-chosen. Axes – both horizontal and vertical axes – are labeled to tell the reader what the histogram is saying. 4/13/2019

TI-84 and Histogram STAT PLOTS has a histogram feature But the screen size is so limited TI-84 histograms might be useful for informal exploratory work TI-84 histograms might be useful for small supplementary illustrations But professional and business situations need something better 4/13/2019

Excel and Histograms Being able to produce professional-looking charts in Excel is a very important today’s world !!!!! It is well worth your time to develop your skills (and learn from your mistakes) NOW in this course, rather than waiting until you’re facing a deadline on a research paper or a workplace project. See separate handouts for helpful info. 4/13/2019

Excel and Histograms You can choose the “Column” chart and do it directly. Or you can have the Data Analysis add-in generate the chart. Either way, 90% of the job is quick & easy. But it will take some thinking and some labor to turn the first graph into something professional. Labels, titles, scaling, styling – these all take time 4/13/2019

Excel and Histograms Excel makes no distinction between Histograms for numerical classes Bar charts for categorical distributions But this course makes a big deal about it Some people “out there” make a big deal about it, too. In many situations, your audience won’t know the difference. 4/13/2019

More resources Link to example with Excel, Insert, Column Link to example with Excel, Data, Data Analysis, Histogram