Summarizing Data in Tables and Graphs

Graphs/Charts for Qualitative Data

Example: Operations Performed at a Hospital last year

Thoracic 20Bones and joints 45Eye, ear, nose, and throat 58General 98Abdominal 115Urologic 74Neurosurgery 23Other 65

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, Ea

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Oth

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Sum

of F

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Bar Graph: displays number or percentage of items in each category using bars

Used for qualitative data

The bars can be vertical or horizontal

The height of a bar represents the quantity we wish to compare

The bars should be of uniform width and uniformly spaced

Graphs/Charts for Quantitative Data

Stem and Leaf – separates data entries into “leading digits” or “stems” and “trailing digits” or “leaves”.

A device that organizes and groups data but allows us to recover the original data if desired

Good for spotting extreme values and patterns

Example: 14 male weights in pounds

139,153,179,201,163,168,157,170,172, 165,145,155,161,151

Frequency distribution – a summary table in which the data are arranged into conveniently established class groupings•useful when dealing with very large data sets•through the grouping process the original

data is lost•should have between 5 and 15 classes•each class grouping should be of equal width•overlapping the classes must be avoided

class midpoint – the point halfway between the boundaries of each class

Weight Number of males130 but less than 140 1140 but less than 150 1150 but less than 160 4160 but less than 170 4170 but less than 180 3180 but less than 190 0190 but less than 200 0200 but less than 210 1Total 14

Histogram – a picture of a frequency distribution

•differs from a bar chart in two waysUsed for quantitative dataThe bars always touch

205195185175165155145135

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Symmetric Uniform

Skewed Right Skewed Left

Bimodal

Symmetrical – both sides are the same when the graph is folded vertically

Uniform – every class has equal frequency (bars are the same height)

Skewed Left or Skewed Right – one tail is stretched longer than the other. The direction of the skewness is on the side of the longer tail.

Bimodal – the two classes with largest frequencies are separated by at least one class (can indicate that we are sampling from two populations)