suppose a biologist studying the mechanical limitations of growth among different species of tulips monitors…

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 inter - quartile range ($iqr$) of the data set. $q_1=square$ cm (do not round) $q_3=square$ cm (do not round) $iqr=square$ cm (do not round)
Answer
Explanation:
Step1: Sort the data
$20, 21, 23, 24, 25, 25, 26, 29, 29, 34$
Step2: Find the position of $Q_1$
$n = 10$, position of $Q_1=\frac{n + 1}{4}=\frac{10+1}{4}=2.75$ $Q_1=21+(23 - 21)\times0.75=22.5$
Step3: Find the position of $Q_3$
Position of $Q_3=\frac{3(n + 1)}{4}=\frac{3\times(10 + 1)}{4}=8.25$ $Q_3=29+(29 - 29)\times0.25=29$
Step4: Calculate the IQR
$IQR=Q_3 - Q_1=29 - 22.5 = 6.5$
Answer:
$Q_1 = 22.5$ cm $Q_3 = 29$ cm $IQR = 6.5$ cm