Question

3.4 Assess Your Understanding

Applying the Concepts #17

17. You Explain It! Quartiles 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 50 states in the United States plus Washington, D.C., in 2012. 01 252.4 2 333.8 Q3 454.5 (a) Provide an interpretation of these results. (b) Determine and interpret the interquartile range. (c) The violent-crime rate in Washington, D.C., in 2012 was 1243.7. Would this be an outlier? (d) Do you believe that the distribution of violent-crime rates is skewed or symmetric? Why?

Answer 1

17.) Solution:-

a.) Ans:-

Interpretation:-from the the give Quartiles we can say 25% of the states have the crime rate, 252.4 crimes per 100000 population or less.

50% of the states have the crime rate, 333.8 crimes per 100000 population or less.

75% of the states have the crime rate, 454.5 crimes per 100000 population or less.

b.)ans:-

Interquartile Range(IQR) =Q_3^-Q₁

_=454.5-252.4

= 202.1 ...ans

c.)Ans:-

Outliers(Upper Fence)= values >Q₃ + 1.5*IQR

=454.5+1.5*202.1

=757.65

here the value (Violent crime rate)=1243.7, which is greater than the value 757.65, hence, the Violent crime rate)=1243.7 is an Outlier.

d.)Ans:-

Skewness=Q3 + Q1 – 2*Q₂

=454.5+252.4- 2*333.8

=39.3

here the value of the Skewness is Positive(>0), hence Violent crime rate is Right Skewed.