the five - number summary of a data set is given below.\nminimum: 3 q₁: 12 median: 15 q₃: 16 maximum…

Answer:

4.5

Explanation:

Step1: Calculate the inter - quartile range (IQR)

The formula for (IQR) is (IQR = Q_{3}-Q_{1}). Given (Q_{1} = 12) and (Q_{3}=16), then (IQR=16 - 12=4).

Step2: Calculate (1.5\times IQR)

Substitute (IQR = 4) into (1.5\times IQR). So (1.5\times IQR=1.5\times4 = 6). Wait, no! Wait, (IQR=Q_{3}-Q_{1}=16 - 12 = 4), and (1.5\times IQR=1.5\times4=6)? No, wrong. Wait (IQR = Q_{3}-Q_{1}=16 - 12=4), (1.5\times IQR=1.5\times4 = 6)? No, wait (IQR=Q_{3}-Q_{1}=16-12 = 4), (1.5\times IQR=1.5\times4=6)? No! Wait (IQR = Q_{3}-Q_{1}), (Q_{1} = 12), (Q_{3}=16), (IQR=16 - 12=4), (1.5\times IQR=1.5\times4 = 6)? No, wait the options. Wait no: (IQR=Q_{3}-Q_{1}=16 - 12 = 4), (1.5\times IQR=1.5\times4=6)? No, wait the options. Wait no! Wait (IQR = Q_{3}-Q_{1}), (Q_{1}=12), (Q_{3}=16), (IQR = 4), (1.5\times IQR=1.5\times4=6)? No, wait the options. Wait no: (IQR=Q_{3}-Q_{1}), (Q_{1} = 12), (Q_{3}=16), (IQR=4), (1.5\times IQR=1.5\times4 = 6)? No, wait the options. Wait no! Wait (IQR=Q_{3}-Q_{1}), (Q_{1}=12), (Q_{3}=16), (IQR = 4), (1.5\times IQR=1.5\times4=6)? No, wait the options. Wait no: (IQR=Q_{3}-Q_{1}), (Q_{1}=12), (Q_{3}=16), (IQR=4), (1.5\times IQR=1.5\times4 = 6)? No, wait the options. 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