Question

suppose a biologist studying the mechanical limitations of growth among different species of tulips monitors a national preserve. he collects data on the heights of 10 different types of tulips in the reserve and rounds each height to the nearest centimeter.
25,21,26,24,29,34,29,25,20,23
compute the first quartile ($q_1$), the third quartile ($q_3$), and the interquartile range ($iqr$) of the data set.
$q_1=\boxed{22}$ cm (do not round)
incorrect answer
$q_3=\boxed{29}$ cm (do not round)
correct answer
$iqr=\boxed{7}$ cm (do not round)
incorrect answer

Explanation:

Step1: Sort the data

$20, 21, 23, 24, 25, 25, 26, 29, 29, 34$

Step2: Find the position of $Q_1$

There are $n = 10$ data - points. The position of $Q_1$ is $i_1=\frac{n + 1}{4}=\frac{10+1}{4}=2.75$. So, $Q_1=23+(24 - 23)\times0.75 = 23.75$ cm.

Step3: Find the position of $Q_3$

The position of $Q_3$ is $i_3=\frac{3(n + 1)}{4}=\frac{3\times(10 + 1)}{4}=8.25$. So, $Q_3=29+(29 - 29)\times0.25 = 29$ cm.

Step4: Calculate the $IQR$

$IQR=Q_3 - Q_1=29 - 23.75 = 5.25$ cm.

Answer:

$Q_1 = 23.75$ cm, $Q_3 = 29$ cm, $IQR = 5.25$ cm