Question

The number of orders received by a food delivery app for 8 consecutive days is as follows.

16, 20, 40, 50, 30, 60, 40, 80.

Find the standard deviation about the mean.

• A. 19.60
• B. 19.73
• C. 19.50
• D. 19.82

Answer 1

The correct option is B

19.73

Let's find the mean first = $\frac{16+20+40+50+30+60+40+80}{8}$

$\overline{x}$ = 42

$\begin{array}{ccccccccc}{x}_i& 16& 20& 40& 48& 30& 60& 40& 80\\ deviation(x-\overline{x})& -26& -22& -2& 6& -12& 18& -2& 38\\ squareofdeviation& 676& 484& 4& 36& 144& 324& 4& 1444\end{array}$

$\therefore Variance=\left(\frac{\sum (X-\overline{x}{)}^2}{N}\right)$

${\sigma }^2=\frac{676+484+4+36+144+324+4+1444}{8}$

$=\frac{3116}{8}=389.5$

Standard deviation = $\sigma =\sqrt{\frac{{\sum }_{i=1}^8(x_i-\overline{x}{)}^2}{8}}$
= $\sqrt{389.5}$ = 19.73

$\therefore$ Standard deviation = 19.73