Answer to Question #103108 in Statistics and Probability for Nimra

Question

Construct a Pareto chart for the number of registered taxicabs in the selected cities.
(City)=new York, Washington,D.C, Chicago, Philadelphia, baltimore.
(Number)=11,787 8348 , 5300 , 1480 , 115

Answer 1

Arrange the data from the largest to smallest according to frequency.

$$\def\arraystretch{1.5} \begin{array}{c:c} City & Number \\ \hline D.C & 8348 \\ \hdashline Chicago & 5300 \\ \hline Philadelphia & 1480 \\ \hline Washington & 787 \\ \hline Baltimore & 115 \\ \hline New York & 11 \end{array}$$

Draw and label the x and y axes. 

Draw the bars corresponding to the frequencies.

The Pareto chart shows that assaults had the highest frequency and homicides the lowest.

$$Total=8348+5300+1480+787+115+11=16041$$

$${8348 \over 16041}\cdot100\%=52.04\%$$

$${5300 \over 16041}\cdot100\%=33.04\%$$ $$52.04\%+33.04\%=85.08\%$$

$${1480\over 16041}\cdot100\%=9.23\%$$ $$85.08\%+9.23\%=94.31\%$$

$${787\over 16041}\cdot100\%=4.91\%$$ $$94.31\%+4.91\%=99.21\%$$

$${115\over 16041}\cdot100\%=0.72\%$$ $$99.21\%+0.72\%=99.93\%$$

$${11\over 16041}\cdot100\%=0.07\%$$ $$99.93\%+0.07\%=100\%$$

$$\def\arraystretch{1.5} \begin{array}{c:c:c} City & Number & Cum. Relative \ Frequencies (\%)\\ \hline D.C & 8348 & 52.04 \\ \hdashline Chicago & 5300 & 85.08 \\ \hline Philadelphia & 1480 & 94.31 \\ \hline Washington & 787 & 99.21 \\ \hline Baltimore & 115 & 99.93 \\ \hline New \ York & 11 & 100 \\ \hline Total= & 16041 & \end{array}$$

Therefore, the following Pareto Chart is obtained based on the table above: