Question

question #7 the educational attainment for 16 different states is listed in the table. find the interquartile range of the data. state % bachelors degree state % bachelors degree arkansas 18.9 oklahoma 22.7 mississippi 19.6 wyoming 34.5 north carolina 26.5 north dakota 25.8 west virginia 17.3 connecticut 35.6 colorado 35.9 nebraska 27.4 indiana 22.5 south carolina 24.3 alabama 22 hawaii 29.6 minnesota 31.5 delaware 28.7 5.5 10.95 7.25 8.3

Explanation:

Step1: Arrange data in ascending order

17.3, 18.9, 19.6, 22, 22.5, 22.7, 24.3, 25.8, 26.5, 27.4, 28.7, 29.6, 31.5, 34.5, 35.6, 35.9

Step2: Find the median (Q2)

Since \(n = 16\) (even), \(Q2=\frac{25.8 + 26.5}{2}=26.15\)

Step3: Find the lower half and Q1

The lower - half is 17.3, 18.9, 19.6, 22, 22.5, 22.7, 24.3, 25.8. Since \(n = 8\) (even), \(Q1=\frac{22+22.5}{2}=22.25\)

Step4: Find the upper half and Q3

The upper - half is 26.5, 27.4, 28.7, 29.6, 31.5, 34.5, 35.6, 35.9. Since \(n = 8\) (even), \(Q3=\frac{29.6+31.5}{2}=30.55\)

Step5: Calculate the inter - quartile range (IQR)

\(IQR = Q3 - Q1=30.55 - 22.25 = 8.3\)

Answer:

8.3