Question

The state of New Jersey is trying to determine whether to add a train line or not, given the new reality of social distancing.Using a selected sample of every fourth person emerging from the PATH train at Newark’s Penn Station, they were only able to find ten people for their sample.Each person was asked how many miles they would drive to work each week, if the trains did not allow for safe social distancing.

The answers were: 150 750 300 425 175 600 450 250 900 275

Calculate the (a) range, (b) the variance, and (c) the standard deviation of the distribution

Answer 1

Answer:

a)

Given,

150 750 300 425 175 600 450 250 900 275

Mean = x/n

= (150 + 750 + 300 + 425 + 175 + 600 + 450 + 250 + 900 + 275) / 10

= 4275 / 10

Mean = 427.5

b)

Variance = ((xi - xbar)^2 / (n-1))

= [ [(150 - 427.5)^2 + (750 - 427.5)^2 + (300 - 427.5)^2 + ...............+ (275 - 427.5)^2] / (10 - 1) ]

= 569312.5 / 9

= 63256.94444

Variance = 63256.94

c)

Standard deviation = sqrt(variance)

substitute variance value

= sqrt(63256.94)

= 251.5093327

Standard deviation = 251.51