Question

Sa of 10 > Suppose a biologist studying the mechanical limitations of growth among different species of tulips monitors a nation preserve. He collects data on the heights of 10 different types of tulips in the reserve and rounds cach height to the nea centimeter. 25, 21,26, 24, 27,30, 29,25, 16,23 Compute the first quartile (Q1). the third quartile (Os), and the interquartile range (IQR) of the data set. 021 cm 03 28 cm IQR 25 cm

Answer 1

The quartiles are computed using the table with the data in ascending order For Q1 we have to compute the following position: 25 25 pos(Qi) -(n +10 (10+175 Since 2.75 is not an integer number, Q1 is computed by interpolating between the values located in the 2th and 3th positions, as shown in the formula below Q1 21 (2.75 -2) x (23- 21) 22.5 For Q3 we have to compute the following position: 75 75 pos(Qs) = (n + 1)-= (10 + 1) = 8.25 Since 8.25 is not an integer number, Q3 is computed by interpolating between the values located in the 8th and 9th positions, as shown in the formula below Q3-27+(8.25-8) x (29- 27) 27.5

So, we have :

$Q_1 =22.5\ cm$

$Q_3 =27.5\ cm$

Now, we use the above values to calculate Inter-Quartile Range:

$IQR = Q_3 - Q_1 = 27.5 - 22.5 = 5\ cm$