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.25,21,26,24,29,33,29,25,19,24Compute the first quartile (Q1), the third quartile (Q3), and the interquartile range (IQR) of the data set.

Answer 1

Answer:
`Q_1=24` ,
`Q_3=29` and IQR= 5

Explanation:

Given : A biologist 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, 33, 29, 25, 19, 24

Arrange in ascending order: 19 , 21 , 24, 24, 25, 25, 26, 29, 29, 33

Lower half = 19 , 21 , 24, 24, 25

Upper half = 25, 26, 29, 29, 33

First quartile
`(Q_1)`= Median of the lower half = 24 (Median is the middlemost value.)

Third quartile
`(Q_3)`= Median of the third half = 29

Interquartile range :
`IQR= Q_3-Q_1=29-24=5`

Hence,
`Q_1=24` ,
`Q_3=29` and IQR= 5