DESCRIPTIVE STATISTICS: GRAPHICAL AND NUMERICAL SUMMARIES

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DESCRIPTIVE STATISTICS GRAPHICAL AND NUMERICAL
SUMMARIES

• Scales of measurement
• Measurements on members of the population
  individuals
• Qualitative or quantitative
• Nominal scale Interval scale
• Ordinal scale Ratio scale
• Precision

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Nominal and Ordinal scales

• Nominal scale individuals classified into groups
  depending on their attributes
• EXAMPLE Gender M or F
• Colors White, Red, Blue.
• Ordinal scale Add order to nominal scale.
• EXAMPLE Grades A, B, C, D, F
• T-shirt size S, M, L, XL.

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Interval and Ratio scales

• Interval scale
• mments are numerical values,
• differences make sense,
• intervals of equal length signify equal
  differences in the characteristic,
• zero does not signify absence of the
  characteristic.
• EXAMPLE temperature.
• Ratio scale
• like interval scale, but
• has absolute zero, i.e. zero means absence of
  the characteristic.
• EXAMPLE height, weight.

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GRAPHICAL SUMMARIES qualitative variables

• Bar chart
• Example. According to the National Center for
  Health Statistics, the 6 leading causes of death
  in 1995 are heart disease, cancer, stroke,
  pulmonary diseases, accidents, and others.

Cause of death Count (k) percent
heart diseases 738 31.92
cancer 538 23.27
stroke 158 6.83
pulmonary diseases 103 4.46
accidents 93 4.02
others 682 29.5
All causes 2,312 100
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GRAPHICAL SUMMARIES qualitative variables

• Pie chart. A disc (pie) is divided into slices
  proportional to the number of observations
  (frequency) in each category.
• Relative frequency for each category. For
  example, heart disease 738/23120.3192 of the
  total.
• Angle corresponding to each category relative
  frequency x 360. For heart disease, 0.3192 x
  360116 degrees.

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GRAPHICAL SUMMARIES Quantitative variables

• HISTOGRAM Shows frequency distribution where
  the values are and how frequently they occur.
• Example Over 50 days a statistics course web
  site had the following number of hits per day
  20, 14, 21, etc. (see text pg.14)
• Frequency Table relative frequency
  frequency/total number of obs.

Class interval Frequency Relative frequency
0 -9 2 0.04
10-19 11 0.22
20 -29 17 0.34
30 -39 9 0.18
40 -49 6 0.12
50 -59 4 0.08
60-69 1 0.02
Total 50 1.00
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GRAPHICAL SUMMARIES Quantitative variables

• Stem and leaf diagram. A bar chart drawn side
  ways.
• Stem 1-2 leading digits.
• Leaves trailing (remaining) digits.
• Example Stem-and-leaf plot for the web site hits
  data
• stem leaves
• 0 89
• 1 1344
• 1 5667789
• 2 0122333
• 2 5566667889
• 3 01223
• 3 5699
• 4 1233
• 4 69
• 5 12
• 5 55
• 6 3