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

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Mathematics for Business Decisions, part I

Histograms

Math 115a

Math 115a


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Histograms Business Decisions, part I

Histograms

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

Math 115a


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Histograms Business Decisions, part I

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


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Histograms Business Decisions, part I

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


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Histograms Business Decisions, part I

Histogram

  • You’ll need to specify:

  • Input Range

  • Bin Range

  • Labels (if applicable)

  • Output Range

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Histograms Business Decisions, part I

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.

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Histograms Business Decisions, part I

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.

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Histograms Business Decisions, part I

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


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Histograms Business Decisions, part I

Bins in Excel

  • Excel will read it as the following:

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Histograms Business Decisions, part I

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


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Histograms Business Decisions, part I

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.

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Histograms Business Decisions, part I

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.

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Histograms Business Decisions, part I

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


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Histograms Business Decisions, part I

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


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Histograms Business Decisions, part I

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”

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Histograms Business Decisions, part I

Graphing window: Data

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Histograms Business Decisions, part I

Graphing window: Series

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Histograms Business Decisions, part I

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!)

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Histograms Business Decisions, part I

Spacing

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

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Histograms Business Decisions, part I

Spacing

  • Right-click on any column

  • Select “Format Data Series”

  • Select the “Options” tab

  • Set “Gap width” to zero

Math 115a