Chapter Objectives

  • Display data graphically and interpret the following graphs: stem-and-leaf plots, line graphs, bar graphs, frequency polygons, time series graphs, histograms, box plots, and dot plots
  • Recognize, describe, and calculate the measures of location of data with quartiles and percentiles
  • Recognize, describe, and calculate the measures of the center of data with mean, median, and mode
  • Recognize, describe, and calculate the measures of the spread of data with variance, standard deviation, and range

Assignment

Percentiles

  • Used to measure location of data
  • Values themselves don’t matter, just as long as they are in order
  • π‘₯th percentile means π‘₯% of data is equal to or lower
  • A value at the 90th percentile means 90% of the data is equal to or below that value

Percentile Equation

Where $k$ is the percentile, $i$ the index (ranking position) of the value in question, and $n$ the total number of values,

\[\begin{align} i &= k(n+1) \end{align}\]

Quartiles

  • Quartiles are percentiles that represent quarters
  • $𝑄_1$ is quartile 1 and is equivalent to the 25th percentile
  • $𝑄_2$ is also know as the median and represents the 50th percentile
  • $𝑄_3$ is the same as the 75th percentile

IQR and Outliers

  • Interquartile Range measures spread of the data
  • Found by subtracting 𝑄_1 from 𝑄_3

Inner Quartile Range

\[\begin{align} \text{IQR} &= Q_3 - Q_1 \end{align}\]
  • Outliers are data points well outside the data set
  • Can determine if an outlier using IQR

Determining Outliers through IQR

An data point is considered an outlier if it is outside the IQR by an amount greater than 1.5 times the IQR.

\[\begin{align} [𝑄_1βˆ’1.5β‹…\text{IQR},𝑄_3+1.5β‹…\text{IQR}] \end{align}\]