Consider the following ordered data: 2 5 5 6 7 8 8 9 10 (a) Find the low, Q1, me

step 1 Question number 6 .A, the low is the smallest value in the data set, so the low is equal to 2. S

Consider the following ordered data: 2 5 5 6 7 8 ...

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

Key Concepts

Interquartile Range

The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1). It measures the spread of the middle 50% of the data, and is less affected by outliers compared to the range, providing a robust indicator of variability.

Quartiles

Quartiles divide an ordered dataset into four equal parts. The first quartile (Q1) represents the 25th percentile, the median (or second quartile) represents the 50th percentile, and the third quartile (Q3) represents the 75th percentile. These measures help in understanding the distribution of the data and its variability.

Box-and-Whisker Plot

A box-and-whisker plot is a graphical representation of the five-number summary. It displays the minimum, Q1, median, Q3, and maximum values, visually summarizing the distribution, spread, and skewness of the data, and highlighting any potential outliers.

Ordered Data

Ordered data refers to the arrangement of data points in increasing or decreasing sequence. This ordering is essential for calculating statistical measures such as the median and quartiles, as it provides the proper context to determine positional statistics within the dataset.

Five-Number Summary

The five-number summary is a set of descriptive statistics that provides a quick overview of the distribution of a dataset. It consists of the minimum (or low), first quartile (Q1), median, third quartile (Q3), and maximum (or high), giving insights into the central tendency, spread, and overall range of the data.

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