Question

The following relative frequency distribution was constructed from a population of 550. Calculate the population mean, the population variance, and the population standard deviation. (Negative values should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.)

Class	Relative Frequency
−20 up to −10	0.30
−10 up to 0	0.22
0 up to 10	0.32
10 up to 20	0.16
Population mean-1.60 (correct) Population variance 115.02 (Its marking this one wrong) Population standard deviation 10.72 (correct)

Answer 1

Solution:

Class	Frequancy (f )	Mid Value (x )	f*x	f * x2
-20-10	0.30	-15	-4.5	67.5
-10-0	0.22	-5	-1.1	5.5
0-10	0.32	5	1.6	8
10-20	0.16	15	2.4	36
Total	n = 1		f*x = 1.6	f * x2 =117

Given that

The mean of sample is

   = fx /n

=  1.6 / 1

   = 1.6

The mean of sample is = 1.60

Population variance is  ²

²  = ( x² - (( x )² / n) n )

  ² = ( 117 - ( (1.6)² / 1) 1

² = ( 117 - 2.56 /1)

² = 114.44 /1

² = 114.44

Population variance is  ² = 114.44

Population standard deviation is

² = ( x² - (( x )² / n) n )

  = ( 117 - ( (1.6)² / 1) 1

= ( 117 - 2.56 /1)

= 114.44 /1

= 114.44

   = 10.6977

Population standard deviation is = 10.70