Question

32. Extracurricular Activities The number of school-related extracurricular activities per student 6 Activities 3 4 0,053 0.084 Probability 0.213 0.059 0.122 0.163 0178 0.128

find the mean,variance, standard deviation of the propability distribution and interpret the results

Answer 1

the probability distribution and calculation table be:-

x	P(x)	$x*P(x)$	$x^2*P(x)$
0	0.059	0.000	0.000
1	0.122	0.122	0.122
2	0.163	0.326	0.652
3	0.178	0.534	1.602
4	0.213	0.852	3.408
5	0.128	0.640	3.200
6	0.084	0.504	3.024
7	0.053	0.371	2.597
TOTAL		$\sum xP(x)=3.349$	$\sum x^2*P(x)=14.605$

the mean be:-

$E(X)=\sum xP(x)$

= 3.349

interpretation:-

on average a student perform 3 school related extracurricular activity.

[ i have not written 3.349, because in real life it is not possible to perform 3.349 activities]

calculation for variance:-

$E(X^2)=\sum x^2P(x)=14.605$

the variance be:-

$var(X)=E(X^2)-E^2(X)$

= (14.605 - 3.349 ²)

$\approx$3.389

interpretation:-

the variance of X is, which is in square units , so we can’t interpret it

the standard deviation be:-

$sd=\sqrt{var(X)}=\sqrt{3.389}$ = 1.841

interpretation:-

the extracurricular activities of students vary by 2 activities on average.

[ here also i have approximated 1.841 ]

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