Math 115a

Mathematics for Business Decisions, part I

Histograms

Math 115a

Math 115a

Histograms

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

Histograms

Test 1 Grade Distribution

0

2

4

6

8

10

40-49 50-59 60-69 70-79 80-89 90-99

Grades (%)

No

. o

f st

ud

ents

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 RangeBin RangeLabels (if applicable)Output Range

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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

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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

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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

Bins in Excel

Math 115a

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Excel will read it as the following:

Bins in Excel

Bin: Understood as:

49 all data points 49

59 49 < data points 59

69 59 < data points 69

79 69 < data points 79

89 79 < data points 89

99 89 < data points 99

Math 115a

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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

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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

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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

labels bins Bin Frequency

40-49 49 49 1

50-59 59 59 8

60-69 69 69 4

70-79 79 79 5

80-89 89 89 7

90-99 99 99 2

More 0

Math 115a

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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

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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

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Graphing window: Data

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Graphing window: Series

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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 0-100. Therefore, it makes sense to demonstrate this continuum of grades by no space between columns:

Spacing

0

1

2

3

4

5

6

7

8

9

40-49 50-59 60-69 70-79 80-89 90-99

Math 115a

Histograms

Right-click on any column

Select “Format Data Series”

Select the “Options” tab

Set “Gap width” to zero

Spacing