# Univariate analysis for Ozone

## Basic summary measures

### Counts

153 values in all, made up of 68 unique values, 116 observed, and 37 missing values.

### Measures of location

Data all 5% trimmed 10% trimmed
Mean 42.1293 40.8839 39.6604

### Quantiles

Quantile Value
0% Minimum 1.00
25% Lower Quartile 18.00
50% Median 31.50
75% Upper Quartile 63.25
100% Maximum 168.00

Measure IQR Standard deviation Variance
Value 45.25 32.9879 1088.2005

## Basic univariate graphs

### Histogram

\begin{Schunk} \begin{figure} \includegraphics{Ozone/Ozone-Hist-1} \caption[The histogram]{The histogram}\label{fig:Hist} \end{figure} \begin{Soutput} This is a histogram, with the title: Histogram of Ozone “Ozone” is marked on the x-axis. Tick marks for the x-axis are at: 0, 50, 100, and 150 There are a total of 116 elements for this variable. Tick marks for the y-axis are at: 0, 10, 20, and 30 It has 9 bins with equal widths, starting at 0 and ending at 180 . The mids and counts for the bins are: mid = 10 count = 37 mid = 30 count = 34 mid = 50 count = 14 mid = 70 count = 15 mid = 90 count = 9 mid = 110 count = 4 mid = 130 count = 2 mid = 150 count = 0 mid = 170 count = 1 \end{Soutput} \end{Schunk}

### Boxplot

\begin{Schunk} \begin{figure} \includegraphics{Ozone/Ozone-Boxplot-1} \caption[The boxplot]{The boxplot}\label{fig:Boxplot} \end{figure} \begin{Soutput} This graph has a boxplot printed horizontally with the title: “” appears on the x-axis. “” appears on the y-axis. Tick marks for the x-axis are at: 0, 50, 100, and 150 This variable has 116 values. An outlier is marked at: 135 168 The whiskers extend to 1 and 122 from the ends of the box, which are at 18 and 63.5 The median, 31.5 is 30 % from the left end of the box to the right end. The right whisker is 3.44 times the length of the left whisker. \end{Soutput} \end{Schunk}

## Assessing normality

### Formal tests for normality

Statistic P Value
Shapiro-Wilk 0.8787 0
Anderson-Darling 4.5211 0
Cramer-von Mises 0.8033 0
Lilliefors (Kolmogorov-Smirnov) 0.1480 0
Pearson chi-square 73.7241 0
Shapiro-Francia 0.8786 0

### Normality plot

\begin{Schunk} \begin{figure} \includegraphics{Ozone/Ozone-NormPlot-1} \caption[The normality plot]{The normality plot}\label{fig:NormPlot} \end{figure} \end{Schunk}

## Formal tests of moments

Statistic Z P Value
D'Agostino skewness 1.226 4.656 0.0000
Anscombe-Glynn kurtosis 4.184 2.203 0.0276