Question

The following table show the qualifying speeds of race cars at the Indianapolis 500.

Speed (mph)	Number of Cars
210 - 215	8
216 - 221	15
222 - 227	32
228 - 233	40
234 - 239	9

Calculate the weighted population standard deviation for this distribution. Round your answer to the nearest hundredth's place and do not indicate units of measure.

Answer 1

Solution:

Class (1)	Frequency (f) (2)	Mid value (x) (3)	f⋅x (4)=(2)×(3)	f⋅x2=(f⋅x)×(x) (5)=(4)×(3)
210-215	8	212.5	1700	361250
216-221	15	218.5	3277.5	716133.75
222-227	32	224.5	7184	1612808
228-233	40	230.5	9220	2125210
234-239	9	236.5	2128.5	503390.25
--	n=104	--	f⋅x=23510	f⋅x2=5318792

Population Standard deviation is σ

=( f x2 ) - (( f x)2 / n ) n

=5318792-(23510)2104 /104

=5318792-5314616.3462/104

=4175.6538/104

=40.1505

=6.336

Population Standard deviation = 6.34