Applied Mathematics for Electrical Engineering (3130908)

Question-5b-OR

BE | Semester-3 Winter-2019 | 26-11-2019

Q5) (b)

In environmental geology computer simulation was employed to estimate how far a block from a collapsing rock wall bounce down a soil slope. Based on the depth, location and angle of block soil impact marks left on the slope of the actual rock fall, the following 10 rebounds lengths (meters) were estimated. Compute mean and standard deviation of the rebounds.
$10.2, 9.5, 8.3, 9.7, 9.5, 11.1, 7.8, 8.8, 9.5, 10 .$

Mean

\bar{x} = \frac{\sum_{} x_{i}}{n} = \frac{10.2 + 9.5 + 8.3 + 9.7 + 9.5 + 11.1 + 7.8 + 8.8 + 9.5 + 10}{10} = \frac{94.4}{10} = 9.44

Standard Deviation

$x$	$x - \bar{x}$	${(x - \bar{x})}^{2}$
$10.2$	$0.76$	$0.5776$
$9.5$	$0.06$	$0.0036$
$8.3$	$- 1.14$	$1.2996$
$9.7$	$0.26$	$0.0676$
$9.5$	$0.06$	$0.0036$
$11.1$	$1.66$	$2.7556$
$7.8$	$- 1.64$	$2.6896$
$8.8$	$- 0.64$	$0.4096$
$9.5$	$0.06$	$0.0036$
$10$	$0.56$	$0.3136$
$\sum {(x_{A} - \bar{x_{A}})}^{2} = 6500$	$\sum {(x_{A} - \bar{x_{A}})}^{2} = 6500$	$\sum {(x - \bar{x})}^{2} = 8.1240$

σ = \sqrt{\frac{\sum {(x - \bar{x})}^{2}}{n}} = \sqrt{\frac{8.1240}{10}} = 0.9013

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