Consider the following ordered data: 2 5 5 ...

Consider the following ordered data:
$$\begin{array}{lllllllll}
2 & 5 & 5 & 6 & 7 & 8 & 8 & 9 & 10 & 12
\end{array}$$
a. Find the low, $Q_{1},$ median, $Q_{3}$ high.
b. Find the interquartile range.
c. Make a box-and-whisker plot.

Key Concepts

Box-and-Whisker Plot

A box-and-whisker plot is a graphical representation of the distribution of a dataset that displays its minimum, first quartile (Q1), median, third quartile (Q3), and maximum values. This plot tool provides a visual summary of the data’s central tendency, spread, and potential outliers, making it easier to understand the data distribution at a glance.

Interquartile Range (IQR)

The interquartile range (IQR) is a measure of statistical dispersion, calculated by subtracting the first quartile (Q1) from the third quartile (Q3). It represents the spread of the middle 50% of the data and is a robust measure of variability that is less affected by outliers compared to the total range.

Quartiles

Quartiles are values that divide a dataset into four equal parts after it has been ordered. Specifically, Q1 is the first quartile (the 25th percentile), the median is the second quartile (the 50th percentile), and Q3 is the third quartile (the 75th percentile). Additionally, identifying the smallest (low/minimum) and largest (high/maximum) values in the dataset provides a complete picture of the data's range.

Ordered Data

Ordered data refers to a dataset that has been arranged in increasing or decreasing order. This organization is crucial for statistical analysis, as many measures of central tendency and dispersion, like medians and quartiles, depend on the data's order to be accurately calculated.

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