GRAPHS AND NUMBERS 1 / 1 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.

VARIABLES 1 / 2 CATEGORICAL QUANTITATIVE Nominal - A, B, C or Fenerbahçe, Galatasaray Ordinal - A > B > C or Fenerbahçe > Galatasaray 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

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

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

IMPORTANCE OF GRAPHS 1 / 10 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!

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

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

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

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. 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. 1/45

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. 1 / 46

VARIANCE and DEVIATION 1/49 EXCEL Example Deviation

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

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). 1/65

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