Quartiles, Percentiles, and IQR for Describing Data

All flashcards

What is the median?

The median is the center value of ordered data that separates the observations into two halves. For an even number of observations, it is the average of the two middle values.

What is $Q_1$?

$Q_1$ is the first quartile, or the midpoint of the lower half of an ordered data set. About one-fourth of the data fall at or below it.

What is $Q_2$?

$Q_2$ is the second quartile. It is the median and corresponds to the 50th percentile.

What is $Q_3$?

$Q_3$ is the third quartile, or the midpoint of the upper half. About three-fourths of the ordered data fall at or below it.

What does a percentile describe?

A percentile describes the relative location of a value in ordered data. The $p$th percentile has approximately $p$ percent of observations equal to or below it; it is not necessarily a percentage score.

Quiz questions

1. For an ordered list of 19 observations, what position does the index method assign to the 25th percentile, using $i=\frac{k}{100}(n+1)$?Answer: The 5th position
2. In a frequency table, what does cumulative relative frequency at a value represent?Answer: The proportion of observations at or below that value
3. A data value has 8 observations below it, 4 equal to it, and the data set contains 20 observations. Using $100\left(\frac{x+0.5y}{n}\right)$, what is its percentile rank?Answer: 50
4. If $Q_1=20$ and $Q_3=60$, what is the upper fence for flagging potential outliers?Answer: 120
5. Which set of values forms a five-number summary?Answer: Minimum, $Q_1$, median, $Q_3$, maximum