Math 115a Mathematics for Business Decisions, part I Histograms Math 115a

Histograms  A histogram is a table/graph that sorts data into pre-specified categories, or bins. Histograms

Math 115a Histograms  You can find Histograms in Excel 2003 under:  Tools  Data Analysis  Histograms  If you don’t see “Data Analysis” under Tools:  Go to Add Ins… under Tools  Select both Analysis Toolpak and Analysis Toolpak-VBA (you may need your original installation disc) Histograms, Excel 2003

Math 115a Histograms  You can find Histograms in Excel 2007 under:  Data tab  Analysis group, Data Analysis  Histograms  If you don’t see the Analysis group in the Data tab:  Go to Add Ins… in Excel Options under the Office button  Select both Analysis Toolpak and Analysis Toolpak-VBA (you may need your original installation disc) Histograms, Excel 2007

Math 115a Histograms Histogram You’ll need to specify:  Input Range  Bin Range  Labels (if applicable)  Output Range

Math 115a Histograms  Input Range:  This is the range of cells that contains the data you want to sort.  Enter this as a typical cell range in Excel: A2:A101, e.g. Histogram window

Math 115a Histograms  Bin Range:  The range of cells that contain your pre-specified bin ranges (i.e. your categories).  Enter this as a typical cell range in Excel: H2:H10, e.g. Histogram Window

Math 115a Histograms  Again, “bins” are your categories that you want to sort your data into.  You must specify the intervals that you want, or else you’ll get some odd endpoints!  Let’s say you want to sort the test scores into the categories 40-49, 50-59, 60-69, …,  You will designate these intervals by the right endpoint for each interval: 49, 59, 69, …, 99 Bins in Excel

Math 115a Histograms  Excel will read it as the following: Bins in Excel Bin:Understood as: 49 all data points  < data points  < data points  < data points  < data points  < data points  99

Math 115a Histograms  Labels  You MUST be consistent:  Check the box: ONLY if you included the column headers for both the input and bins.  Leave unchecked: ONLY if your ranges contained only the data, and no headers. Histogram Window

Math 115a Histograms  Output Range  Input only the cell in which you want the output to START. You should have several clear columns to the right of this cell, and several empty cells below this.  NOTE: By default, “New Worksheet Ply:” is selected. When you choose “Output Range” it will automatically highlight the “Input Range” space. BE CAREFUL! You click in the box by “Output Range” before selecting a cell. Histogram Window

Math 115a Histograms  The output from Excel repeats your bin limits, and also gives the frequency count.  “More” should be zero. If not, your bin limits did not go high enough to accommodate your data. Output labelsbins BinFrequency More0

Math 115a Histograms  Bins do not need to start at zero!  Find the range of your data  range = maximum – minimum  Your first bin limit should be reasonably above your minimum data point  Good rule-of-thumb: your first bin limit should be equal to your minimum value + bin width  Your last bin limit should be greater than your maximum data point Choosing appropriate bin limits

Math 115a Histograms  Rule of thumb: start your bin size by the calculation: range of data  10  Make your endpoints nice numbers, but make sure every bin has the same size interval  See how your histogram looks:  If it’s too “blocky”, increase the number of bins by decreasing the bin size  If it’s too detailed, decrease the number of bins by increasing the bin size Choosing the bin size

Math 115a Histograms  Histograms are typically shown as a column graph.  Use Excel’s Chart Wizard  Select Column Graph as the type  In “Data Range” select only the non-More Frequency cells.  Click on the “Series” tab and enter the range of cells for labels for “X-axis labels” Graphing the histogram

Math 115a Histograms Graphing window: Data

Math 115a Histograms Graphing window: Series

Math 115a Histograms  NOTE: Labels will always be centered under each column. Therefore it is not a good idea to label a column by its right endpoint. Labeling by the full interval (i.e. “40-49”) is acceptable only if you have enough room, and not too many bins. Usually it is best to have a column of midpoints for each interval, and label with these. (Remember, the label is centered under each column!) Labels

Math 115a Histograms  We know grades can range from Therefore, it makes sense to demonstrate this continuum of grades by no space between columns: Spacing

Math 115a Histograms  Right-click on any column  Select “Format Data Series”  Select the “Options” tab  Set “Gap width” to zero Spacing