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

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.

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.

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

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 738/2312=0.3192 of the total. Angle corresponding to each category= relative frequency x 360. For heart disease, 0.3192 x 360=116 degrees.

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

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