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

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histograms

Mathematics for Business Decisions, part I

Histograms

Math 115a

Math 115a

slide2

Histograms

Histograms

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

Math 115a

slide3

Histograms

Histograms, Excel 2003

  • 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)

Math 115a

slide4

Histograms

Histograms, Excel 2007

  • You can find Histograms in Excel 2007 under:
    • Data tab
      • Analysis group, Data Analysis
        • Histograms
  • If you don’t see the Analysis groupin 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)

Math 115a

slide5

Histograms

Histogram

  • You’ll need to specify:
  • Input Range
  • Bin Range
  • Labels (if applicable)
  • Output Range

Math 115a

slide6

Histograms

Histogram window

  • 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.

Math 115a

slide7

Histograms

Histogram Window

  • 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.

Math 115a

slide8

Histograms

Bins in Excel

  • 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, … , 90-99.
    • You will designate these intervals by the right endpoint for each interval: 49, 59, 69, …, 99

Math 115a

slide9

Histograms

Bins in Excel

  • Excel will read it as the following:

Math 115a

slide10

Histograms

Histogram Window

  • 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.

Math 115a

slide11

Histograms

Histogram Window

  • 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.

Math 115a

slide12

Histograms

Output

  • 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.

Math 115a

slide13

Histograms

Choosing appropriate bin limits

  • 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

Math 115a

slide14

Histograms

Choosing the bin size

  • 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

Math 115a

slide15

Histograms

Graphing the histogram

  • 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”

Math 115a

slide16

Histograms

Graphing window: Data

Math 115a

slide17

Histograms

Graphing window: Series

Math 115a

slide18

Histograms

Labels

  • 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!)

Math 115a

slide19

Histograms

Spacing

  • We know grades can range from 0-100. Therefore, it makes sense to demonstrate this continuum of grades by no space between columns:

Math 115a

slide20

Histograms

Spacing

  • Right-click on any column
  • Select “Format Data Series”
  • Select the “Options” tab
  • Set “Gap width” to zero

Math 115a

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