Answer to Question #347796 in Statistics and Probability for Henry

Question

Find the range, variance, and standard deviation unless the question asks for something different.

Passenger Vehicle Deaths. The number of people killed in each state from passenger vehicle

crashes for a specific year is shown

778 309 1110 324 705

1067 826 76 205 152

218 492 65 186 712

193 262 452 875 82

730 1185 2707 1279 390

305 123 948 343 602

69 451 951 104 985

155 450 2080 565 875

414 981 2786 82 793

214 130 396 620 797

Answer 1

Sorted Data Set: 65, 69, 76, 82, 82, 104, 123, 130, 152, 155, 186, 193, 205, 214, 218, 262, 305, 309, 324, 343, 390, 396, 414, 450, 451, 452, 492, 565, 602, 620, 705, 712, 730, 778, 793, 797, 826, 875, 875, 948, 951, 981, 985, 1067, 1110, 1185, 1279, 2080, 2707, 2786.

$$Range=2786-65=2721$$

$$mean=\bar{x}=\dfrac{1}{50}\displaystyle\sum_{i=1}^{50}x_i=631.98$$

$$Var(X)=\sigma^2=\dfrac{1}{50}\sum_{i=1}^{50}(x_i-\bar{x})^2$$ $$=348319.0196$$

$$\sigma=\sqrt{\sigma^2}=\sqrt{348319.0196}\approx590.18558$$