In: Math
Scores: 57, 49, 53, 60, 58, 59, 48,
Solution:
Given that
x | x2 |
57 | 3249 |
49 | 2401 |
53 | 2809 |
60 | 3600 |
58 | 3364 |
59 | 3481 |
48 | 2304 |
∑x=384 | ∑x2=21208 |
a ) The sample mean is
Mean
= (
x/
n) )
= ( 57+49+ 53+ 60+ 58+ 59,+48 / 7 )
= 384 / 7
= 54.8571
Mean
= 54.8571
b ) Median :
Observations in the ascending order are :
48,49,53,57,58,59,60
Here, n = 7 is even
M = Value of ( n + 1 / 2) Observation.
= Value of ( 7 + 1 / 2) Observation.
= Value of 4th Observation.
= 57
Median = 57
c ) Population standard deviation =
=
(
x2 ) - ((
x )2 / n ) / n )
=
21208- ( 384 /7 )2 / 7
=
21208--
21065.1429 / 7
=
142.8571 / 7
=
2040.82
= 4.5175
Population standard deviation = 4.5175