Question

Refer to the accompanying table, which describes the number of adults in groups of five who reported sleepwalking. Find the mean and standard deviation for the numbers of sleepwalkers in groups of five. 

Click the icon to view the data table. 

The mean is _______  sleepwalker(s). 

The standard deviation is _______ sleepwalker(s). 

Answer 1

Random variable X = no . of adults who are sleepwalking in group of 5 .

possible values of X =0,1,2,3,4,5

Probability distribution for X is given as:

x	P(x)
0	0.191
1	0.353
2	0.299
3	0.124
4	0.031
5	0.002

   Mean of a discrete random variable X is given as:

  

Mean = 0 * 0.191 + 1 * 0.353 + 2* 0.299 ----------+ 5* 0.002 = 1.457 = 1.5 sleepwalkers

Standard deviation is a measure of variability of data and gives how much data is dispersed around mean value.

For a ramdom variable , Standard deviation is given as :

  

= Mean

So , S.D =

Standard Deviation = 1.043 = 1.0