Question

The following relative frequency distribution was constructed from a population of 650. Calculate the population mean, the population variance, and the population standard deviation.

Class	Relative Frequency
−20 up to −10	0.30
−10 up to 0	0.20
0 up to 10	0.40
10 up to 20	0.10

Population Mean -

Population Variance -

Population Standard Deviation -

Answer 1

Solution:

Given that,

Class	Frequency	Relative Frequency	Mid value	fx	fx2
−20 up to −10	0.30*650 = 195	0.30	-15	-2925	43875
−10 up to 0	0.20 * 650 = 130	0.20	-5	-650	3250
0 up to 10	0.40 = 260	0.40	5	1300	6500
10 up to 20	0.10 = 65	0.10	15	975	14625
Total	N = 650			fx = -1300	fx2 = 68250

a ) The population mean is    

=  fx / N

= -1300 / 650

= - 2

The population mean is   = - 2

b ) Population Variance is  ²

² =   ( fd² ) - (( fd )² / N ) / N

   = ( 68250 ( (- 1300 )² / 650 ) / 650

   = ( 68250 -2600 ) / 650

= 65650*/650

= 101

Population Variance is  ² = 101

C ) Population Standard Deviation is

= Variance

= 101

= 10.0499

Population Standard Deviation = 10.0499