Question

1. For the following distribution find the mean, median, mode, range and standard deviation:

13, 10, 16, 20, 10, 14, 13, 25

Answer 1

Solution:

x	x2
13	169
10	100
16	256
20	400
10	100
14	196
13	169
25	625
x = 121	x2 = 2015

a ) The sample mean is

Mean   = (x / n) )

= (13 + 10 + 16+ 20 +10 +14 + 13 +25 / 8 )

= 121 / 8

= 15.125

Mean   = 15.12

b ) Median

Observations in the ascending order are :

Here, n = 8 is even

M = (value of (n / 2 )^th Observations + value of (n / 2 + 1 )^th Observations ) / 2

   = (value of (8/ 2 )^th Observations + value of (8 / 2 + 1 )^th Observations) / 2

= (value of 4^th Observations + value of 5^th Observations) / 2

= (13 + 14 ) / 2

= 27 / 2

= 13.5

Median = 13.5

c ) Mode :
In the given data, the observation 10, 13  occurs maximum number of times ( 2 )

Z = 10, 13

d ) The range = Maximum value- Minimum vaLue

= 25 - 10

= 15

The range = 15

e ) The sample standard is S

  S = ( x² ) - (( x)² / n ) n -1

= (2015( (121 )² / 8 ) 7

   = (2015 - 1830.125 / 7)

= (184.875 / 7 )

= 26.4107

= 5.1391

The sample standard is = 5.14