Lec 4 - Exploring numeric data

STAT 1010 - Fall 2022

Learning outcomes

By the end of this lesson you should:

• Understand measures of center and know how to compute them

• Understand measures of spread and know how to compute them

• Graphical representation and interpretation of one numerical variable in R

Definition of numeric variable

A numeric or quantitative variable is a variable that can be measured.

The purpose of Exploratory Data Analysis (EDA)

• EDA is about learning the structure of a dataset through a series of numerical and graphical techniques.

• When you do EDA, you’ll look for both

  • general trends and

  • interesting outliers in your data.

generate questions that will help inform subsequent analysis.

Observations

Variables

Measures of center

• Mean

• Median (\(50\%th\) percentile)

Mean

\(\overline{var} =\frac{the\; sum\; of\; all\; the\; observations\; in\; the \; var}{the \; number \;of \;observations}\)

Mean vs median

Mean vs median

Mean - sensitive to outliers and skewed distributions

Median - more stable estimate

Mode - most common value

Measures of spread

• Percentiles

  • quartiles

  • Interquartile range

• variance \(s^2\)

• standard deviation \(s\)

• range

Variance

\(s_{var}^2 =\frac{(observation\; 1 \; in\; the \; var - \overline{var})^2 + (observation\; 2 \; in\; the \; var - \overline{var})^2 + \dots + (observation\; n \; in\; the \; var - \overline{var})^2}{the \; number \;of \;observations - 1}\)

Graphically

A few of the “squares”

Due to the aspect ratio of the plot these squares are not square. Ask the students if these are really squares or not.

Standard deviation

\(s_{var} =\sqrt{\frac{(observation\; 1 \; in\; the \; var - \overline{var})^2 + (observation\; 2 \; in\; the \; var - \overline{var})^2 + \dots + (observation\; n \; in\; the \; var - \overline{var})^2}{the \; number \;of \;observations - 1}}\)

Words to know

• mean
• median or quartile 2 (Q2)
• lower quartile (LQ) or quartile 1 (Q1)
• upper quartile (UQ) or quartile 3 (Q3)
• interquartile range (IQR)

Your turn

Click here or the qr code below to write your first line of code