DESCRIPTIVE STATISTICS: GRAPHICAL AND NUMERICAL SUMMARIES
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Presentation on theme: "DESCRIPTIVE STATISTICS: GRAPHICAL AND NUMERICAL SUMMARIES"— Presentation transcript:
1 DESCRIPTIVE STATISTICS: GRAPHICAL AND NUMERICAL SUMMARIES Scales of measurementMeasurements on members of the population – individualsQualitative or quantitativeNominal scale Interval scaleOrdinal scale Ratio scalePrecision
2 Nominal and Ordinal scales Nominal scale: individuals classified into groups depending on their attributesEXAMPLE: Gender: M or FColors: White, Red, Blue.Ordinal scale: Add order to nominal scale.EXAMPLE: Grades: A, B, C, D, FT-shirt size: S, M, L, XL.
3 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, buthas “absolute zero”, i.e. zero means absence of the characteristic.EXAMPLE: height, weight.
4 GRAPHICAL SUMMARIES: qualitative variables Bar chartExample. 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 deathCount(k)percentheart diseases73831.92cancer53823.27stroke1586.83pulmonary diseases1034.46accidents934.02others68229.5All causes2,312100
5 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= of the total.Angle corresponding to each category= relative frequency x 360. For heart disease, x 360=116 degrees.
6 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 intervalFrequencyRelative frequency0 -920.0410-19110.2220 -29170.3430 -3990.1840 -4960.1250 -5940.0860-6910.02Total501.00
7 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 datastem leaves6 3