Question

Violent crimes include rape, robbery, assault, and homicide. The following is a summary of the violent-crime rate (violent crimes per 100,000 population) for all states of a country in a certain year. Complete parls (a) through (d). Q4 = 273.8, Q. = 388.5, Q7 = 529.7 (a) Provide an interpretation of these results. Choose the correct answer below. O A. 25% of the states have a violent-crime rate that is 273.8 crimes per 100,000 population or more. 50% of the states have a violent-crime rate that is 388.5 crimes per 100,000 population or more. 75% of the states have a violent-crime rate that is 529.7 crimes per 100.000 population or more. OB. 25% of the states have a violent-crime rate that is 273.8 crimes per 100,000 population or less. 50% of the states have a violent-crime rate that is 388.5 crimes per 100,000 population or less. 75% of the states have a violent-crime rate that is 529.7 crimes per 100.000 population or less. OC. 75% of the states have a violent-crime rate that is 273.8 crimes per 100.000 population or less. 50% of the states have a violent-crime rate that is 388.5 crimes per 100.000 population or less. 25% of the states have a violent-crime rate that is 529.7 crimes per 100,000 population or less (b) Determine and interpret the interquartile range. The interquartile range is crimes per 100,000 population. (Type an integer or a decimal.) Interpret the interquartile range. Choose the correct answer below. O A The middle 25% of all observations have a range of 255.9 crimes per 100,000 population. OB. The middle 50% of all observations have a range of 114.7 crimes per 100,000 population. OC. The middle 50% of all observations have a range of 255.9 crimes per 100,000 population. OD. All observations have a range of 255.9 crimes per 100.000 population. (c) The violent-crime rate in a certain state of the country in that year was 1,679. Would this be an outlier? The lower fence is crimes per 100,000 population. The upper fence is crimes per 100,000 population (Round to two decimal places as needed.) Click to select your answers)

Answer 1

a). 25% of the states have a violent crime rate that is 273.8 crimes per 100000 population or less, 50% of teh states have a violent crime rate that is 388.5 crimes per 100000 population or less. 75% of the states have a violent crime rate that is 529.7 crimes per 100000 population or less. (B)

b). The interquartile range is 255.9 crimes per 100000 population.

[ IQR = (Q₃-Q₁) = (529.7- 273.8) = 255.9 ]

Interpretation:-

the middle 50% of the observations have a range of 255.9 crimes per 100000 population. (C)

c). the lower fence is -110.05 crimes per 100000 population.

[ lower fence = Q₁ -(1.5*IQR) = 273.8 - (1.5*255.9) = -110.05 ]

the upper fence is 913.55 crimes per 100000 population.

[ upper fence = Q₃+(1.5*IQR) = 529.7 + (1.5*255.9) = 913.55 ]

YES, 1679 is an outlier.

[ as this is greater than the upper fence, i.e, 913.55 ]

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