Question

Railroad Crossing Accidents The data show the number of railroad crossing accidents for the 50 states of the United States for a specific year. Construct a histogram, frequency polygon, and ogive for the data. Comment on the skewness of the distribution. (The data in this exercise will be used for Exercise 15 in this section.)

Answer 1

$$\def\arraystretch{1.5} \begin{array}{c:c} Class \ limits& Frequency \\ \hline 1-43 & 24 \\ \hdashline 44-86 & 17 \\ \hdashline 87-129 & 3 \\ \hdashline 130-172 & 4 \\ \hdashline 173-215 & 1 \\ \hdashline 216-258 & 0 \\ \hdashline 259-301 & 0 \\ \hdashline 302-344 & 1 \\ \hdashline \end{array}$$

$$\def\arraystretch{1.5} \begin{array}{c:c:c:c} Class & Class & Midpoint & Relative \\ limits & boundaries & & frequency \\ \hline 1-43 & 0.5-43.5 & 22 & 0.48 \\ \hdashline 44-86 & 43.5-86.5 & 65 & 0.34 \\ \hdashline 87-129 & 86.5-129.5 & 108 & 0.06 \\ \hdashline 130-172 & 129.5-172.5 & 151 & 0.08 \\ \hdashline 173-215 & 172.5-215.5 & 194 & 0.02 \\ \hdashline 216-258 & 215.5-258.5 & 237 & 0 \\ \hdashline 259-301 & 258.5-301.5 & 280 & 0 \\ \hdashline 302-344 & 301.5-344.5 & 323 & 0.02 \\ \hdashline \end{array}$$

$$\def\arraystretch{1.5} \begin{array}{c:c:c} & Cumulative & Cumulative \\ & frequency & relative frequency \\ \hline <0.5 & 0 & 0.00 \\ \hdashline <43.5 & 24 & 0.48 \\ \hdashline <86.5 & 41 & 0.82 \\ \hdashline <129.5 & 44 & 0.88 \\ \hdashline <172.5 & 48 & 0.96 \\ \hdashline <215.5 & 49 & 0.98 \\ \hdashline <258.5 & 49 & 0.98 \\ \hdashline <301.5 & 49 & 0.98 \\ \hdashline <344.5 & 50 & 1.00 \\ \hdashline \end{array}$$

Histogram for number of railroad crossing accidents

Frequency polygon for number of railroad crossing accidents

Ogive for number of railroad crossing accidents

Mean>mode. Right-skewed (positive) distribution.