Violent crimes include rape, robbery. assault, and homicide. The following is a

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 parts (a) through (d). 01 -271.8, Q2 3874, Q3 529.7 (a) Provide an interpretation of these results. Choose the correct answer below. OA. O B OC 25%of estates have a len rime rate that s 2718cr mes per 00000 population or more 5 % ofthe states have a olen rime rate that s 74 crimes er10,00 population roe 75 So he state have a violent-crime rate that is 529.7 crimes per 100,000 population or more. 75% o the states have a violent crime rate hat s 271 8 crimes per 100 000 population or less 50% o the states have a violent crime rate that is 387 4 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. 25%ofthe states have a violent crime rate at s2718c mes per 0000 population or ess.2 %ofthe states have av o enter me rate has 874cr mes er 0000population or ess. S 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.) nterpret the interquartile range. Choose the correct answer below. O A. OB. ° C. The middle 50% of all observations have a range of 1 15.6 crimes per 100,000 population All observations have a range of 257.9 crimes per 100,000 population. The middle 50% of all observations have a range of 257.9 crimes per 100,000 population. D. The middle 25% of all observations have a range of 257.9 crimes per 100.000 population

Explanation / Answer

Q1 means below Q1 there is 25% observations

so 25% observations have values less than or equal to Q1

so the answer is C

b)inter quantile range = Q3-Q1=257.9

the options is again C

because in Q1 and Q3 there is 50% observations and we are taking a difference

lower fence= Q1 – (1.5 * IQR)=271.8-1.5*257.9=-115.05

upper fence= Q3 + (1.5 * IQR)=529.7+1.5*257.9=916.55

yes the given number is outlier as it is greater than the outer fence

skewness= Q3 + Q1 – 2Q2=529.7+271.8-2*387.4=26.7>0

so positively skewed

we have used Bowleys measure of skewness

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