Descriptive statistics help us organize, summarize, and interpret a set of data. In this lesson, you will investigate the number of pairs of shoes owned by a sample of classmates and learn how graphs and numerical measures describe that data.
Survey 30 classmates and record the number of pairs of shoes each person owns. Each recorded number is a data value, and the complete collection of values is a data set. Because the values are counts of pairs, they are discrete: they can be whole numbers, not fractions of a pair.
All flashcards
What is a histogram?
A graph that groups numerical data into intervals and uses touching bars to show the frequency in each interval.
What does the sample standard deviation, s, measure?
It describes the typical distance of observations from the sample mean. Larger values generally indicate more spread around the mean.
What is the five-number summary?
The minimum, first quartile (Q1), median (M), third quartile (Q3), and maximum.
What does the IQR represent?
The interquartile range, Q3−Q1, measures the spread of the middle 50% of the data.
How does the 1.5-IQR rule flag potential outliers?
Values below Q1−1.5(IQR) or above Q3+1.5(IQR) are flagged as potential outliers for further investigation.
Quiz questions
Why is the number of pairs of shoes owned classified as discrete data?Answer: It is a count that takes whole-number values rather than any value on a continuous scale.
What does the sample standard deviation describe?Answer: The typical spread of data values around the sample mean.
A data set has Q1=8 and Q3=14. What is its interquartile range?Answer: 6
A value is above the upper 1.5-IQR fence. What is the appropriate interpretation?Answer: It is a potential outlier that should be examined in context.
Why do the bars in a histogram touch?Answer: They represent adjacent intervals along a numerical scale.
Based on Introductory Statistics 2e by Barbara Illowsky, Susan Dean (OpenStax), licensed CC BY 4.0. Adapted into a summary, flashcards and quizzes.