Applied Mathematics for Electrical Engineering (3130908)

Question-5a-OR

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

Q5) (a)

The pH solution is measured eight times using the same instrument and data obtained are as follows:

$7.15, 7.20, 7.18, 7.19, 7.21, 7.20, 7.16, 7.18$

Calculate the mean, variance and standard deviation.

Mean

\bar{x} = \frac{\sum_{} x_{i}}{n} = \frac{7.15 + 7.20 + 7.18 + 7.19 + 7.21 + 7.20 + 7.16 + 7.18}{8} = \frac{57.47}{8} = 7.1838

Standard Deviation

$x$	$x - \bar{x}$	${(x - \bar{x})}^{2}$
$7.15$	$- 0.0338$	$0.0011$
$7.20$	$0.0162$	$0.0003$
$7.18$	$- 0.0038$	$0.00001$
$7.19$	$0.0062$	$0.00004$
$7.21$	$0.0262$	$0.0007$
$7.20$	$0.0162$	$0.0003$
$7.16$	$- 0.0238$	$0.0006$
$7.18$	$- 0.0038$	$0.00001$
$\sum {(x_{A} - \bar{x_{A}})}^{2} = 6500$	$\sum {(x_{A} - \bar{x_{A}})}^{2} = 6500$	$\sum {(x - \bar{x})}^{2} = 0.0031$

σ = \sqrt{\frac{\sum {(x - \bar{x})}^{2}}{n}} = \sqrt{\frac{0.0031}{8}} = 0.0197

Variance

σ^{2} = {(0.0197)}^{2} = 0.0004

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