Question

Task 4 make your own experiment and trial .choose your own random variable X and compute for its mean , variance and standard deviation

Answer 1

Solution

Let $X$ represent the marks of $7$ students in a test

$X=66,73,59,62,69,65,70$

(a) mean $\bar X=\dfrac{\sum X_i}n$

$\bar X=\frac{66+73+59+62+69+65+70}{7}$

$\bar X=\dfrac{464}7=66.288$

(b) Variance

$~~~~~~~\def\arraystretch{1.5}\begin{array}{c:c:c}X_i &X_i -\bar X& (X_i -\bar X)^2\\\hline59&-7.288&53.115\\\hdashline62&-4.288&18.387\\\hdashline65&-1.288&1.659\\\hdashline66&-0.288&0.083\\\hdashline69&2.712&7.355\\\hdashline70&3.712&13.779\\\hdashline73&6.712&45.051\\\hline\sum&&139.429\\\hline\end{array}$

$\sigma^2=\dfrac{139.429}7=19.92$

(c) Standard deviation

$\sigma=\sqrt{variance}$

$\sigma=\sqrt{19.92}$

$\sigma=4.463$