3A: Exploratory Data Analysis: One Variable

Appropriate Uses for One Variable Data Displays

• If it’s a categorical variable, use a frequency distribution table

  • Can also use bar charts and pie charts

• If it’s a quantitative variable, use histograms, boxplots, and measures of center & spread

Categorical Data Display: Frequency Distribution

Table with counts that lists every observation and the category it falls under

• Relative frequency distributions convert frequency into percentages

Appropriate Uses for Quantitative Data Measures

• If data is symmetric, use mean and standard deviation

• If data is skewed, use median and IQR

Measures of Center: Mean

Average of the values

• Sensitive to outliers

Measures of Center: Median

Middle observation in a data set of N observations ordered smallest to largest

• Odd data set, median is the ((N + 1)/2)th term

• Even data set, median is between the (N/2)th and the ((N + 1)/2)th term

• Resistant to outliers

Measures of Center: Mode

Most common datapoint

• Resistant to outliers

Measures of Spread: Range

Difference between the minimum and maximum value

• Sensitive to outliers

Measures of Spread: Interquartile Range (IQR)

Four equal groups analyzing data ordered smallest to largest

• 25% data points below Q1

• 50% data points below Q2; Q2 = Median

• 75% data points below Q3

• Outliers are outside the “upper” and “lower” limits

IQR Formulas

• IQR = Q3 - Q1

• Upper Limit = Q3 + (1.5 * IQR)

• Lower Limit = Q1 - (1.5 * IQR)

Measures of Spread: Standard Deviation

Difference from some data point and the mean of the data set

• Sensitive to outliers

Quantitative Data Displays: Histogram

Frequency distribution chart but with vertical boxes that cover different intervals

Histogram Features: Shape

• Uniform: flat line (every var has equal frequency)

• Bell-shaped is self explanatory

• Skewed-right: cluster at left, “tail” to the right

  • Mean pulled right; mean > median

• Skewed-left: cluster at right, “tail” to the left

  • Mean pulled left; median > mean

The Empirical Rule of Bell-shaped Distribution

• 68% of data is one standard deviation from the mean (μ ± σ)

• 95% of data is two standard deviations away (μ ± 2σ)

• 99.7% of data is three standard deviations away (μ ± 3σ)

Quantitative Data Display: Boxplot

Box over a number line with a horizontal line going through it

• Vertical lines signify Min → Q1 → Median (Q2) → Q3 → Max