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GRAPHS AND NUMBERS

1 / 1. GRAPHS AND NUMBERS. As we study graphs and numerical summaries, we keep firmly in mind where the data come from and what we hope to learn from them. Graphs and numbers are not ends in themselves, but aids to understanding. 1 / 2. VARIABLES. CATEGORICAL.

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GRAPHS AND NUMBERS

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  1. 1 / 1 GRAPHS AND NUMBERS As we study graphs and numerical summaries, we keep firmly in mind where the data come from and what we hope to learn from them. Graphs and numbers are not ends in themselves, but aids to understanding.

  2. 1 / 2 VARIABLES CATEGORICAL Nominal - A, B, C or Fenerbahçe, Galatasaray Ordinal - A > B > C or Fenerbahçe> Galatasaray QUANTITATIVE Interval - (B - A) = (C - B) Zero is any other number. e.g. Celsius scale Ratio - B = n A B is n times as much as A Zero means nothing, nil. e.g. Kelvin scale

  3. 1 / 5 ALWAYS ASK • What variables were measured? • What are the units of measurement? • Are the data coded?

  4. 1 / 6 VARIABILITY of AVERAGES Averages are always less variable than measurements because chance errors are balanced out! The more your measurements, the better your statistics.

  5. 1 / 10 IMPORTANCE OF GRAPHS Making a graphical display is the first step toward understanding data; performing well-chosen calculations is the second. A picture is worth a thousand numbers!

  6. 1 / 13 HISTOGRAMS Histogram In EXCEL : Tools Data Analysis If Data Analysis is not on the Tools menu then Tools Add-ins Analysis ToolPAk EXCEL Example Histogram

  7. 1/16-20 GRAPHS In EXCEL : Insert Chart ... Play around with different types of charts. EXCEL Example Graphs

  8. 1/39 MEAN vs MEDIAN shown with bar. Not a resistant statistic of center. Use with no outliers. Median - resistant measure of center.

  9. 1/45 STEMPLOTS vs BOXPLOTS • Stemplots/histograms show distribution. • Use for a single set of data. • Boxplots show median and spread. • Use for comparing sets of data.

  10. 1/45 REGULARITY Measures based on routine methods of statistics (e.g. mean. standard deviation) are generally meaningful only for distributions of sufficiently regular shape. Quickly resorting to fancy calculations is the mark of a statistical amateur.

  11. 1 / 46 WHY (n - 1) AND NOT n can be computed from the first n - 1 values when the mean is known, i.e. is dependent on them.

  12. 1/49 VARIANCE and DEVIATION EXCEL Example Deviation

  13. 1/60 WHY DENSITY CURVE? Each bag 10 kg 1 meter 25 kg

  14. 1/65 ASSUMPTION of NORMALITY • Good for: • Means of samples. • Data from large populations. • Repeated measures. • Random phenomena. • NOT good for: • Individual variables (income, service life, etc).

  15. 1/73 ASSESSING NORMALITY FIRST Look at stemplot or histogram for: Skew. Gaps. Outliers. SECOND Test for 68 - 95 - 99.5 rule. THIRD Plot normal quantile plot. EXCEL Example NQ Plot

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