First slide

Introduction to statistics

Question

The mean and the SD of 1,2,3,4,5,6 are

Easy

A

$\frac{7}{2}, \sqrt{\frac{35}{12}}$
B

$3, 3$
C

$\frac{7}{2}, \sqrt{3}$
D

$3, \frac{35}{12}$

Solution

$Mean \bar{x} = \frac{1 + 2 + 3 + 4 + 5 + 6}{6} = \frac{21}{6} = \frac{7}{2}$
$\begin{array}{l} SD = σ = \sqrt{\frac{1}{n} \sum_{i}^{2} - (\bar{x})^{2}} \\ = \sqrt{\frac{1}{6} (1 + 4 + 9 + 16 + 25 + 36) - \frac{49}{4}} \\ = \sqrt{\frac{91}{6} - \frac{49}{4}} = \sqrt{\frac{182 - 147}{12}} = \sqrt{\frac{35}{12}} \end{array}$

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