Question

The following is a list of prices paid (in dollars) by the elderly for antidepressant medication. 20, 42, 34, 31, 17, 21, 53, 34, 19, 55, 23, 57, 34, 61, 44, 41, 39, 38, 47, 30 What is the mean amount paid by the elderly for antidepressant medication (rounded to a whole number)? What is the median, standard deviation, range and variance

Answer 1

Sort given sample in ascending order.

17 , 19 , 20 , 21 , 23 , 30 , 31 , 34 , 34 , 34 , 38 , 39 , 41 , 42 , 44 , 47 , 53 , 55 , 57 , 61

a)

Mean = X / n

= 740 / 20

= 37

b)

Median = (n+1) / 2th observation

= (20+1) / 2 th observation

= 10.5th observation

= 36

c)

Variance = ( X² - n * mean² )/ n-1

= ( 30708 - 20 * 37² ) / 19

= 175.158

d)

Standard deviation = Sqrt( Variance )

= Sqrt( 175.158)

= 13.235

e)

Range = Largest value - Smallest value

= 61 - 17

= 44