Question

Listed below are speeds (in mi/h) of cars on the New Jersey Turnpike by race of the driver. All cars are going in the same direction, and all of the cars are from New Jersey. The data are from Statlib and the authors are Joseph Kadane and John Lamberth. Find Variance and find the standard deviation. 79 70 71 76 76 74 71 75 74 74 Var=745-2.749 O 5-2.749. Var 7.55 O mean - 745 2.749 mean -7.45 2.749

Answer 1

Solution :

The variance is given as follows :

$\large Variance = \frac{1}{n-1}\sum_{i=1}^{n}(x_{i}-\bar{x})^{2}$

Where, xi's are given values, n is number of observations and x̄ is sample mean.

$\large \bar{x} = \frac{1}{n}\sum_{i=1}^{n}x_{i}$

We have, n = 10

$\large \bar{x} = \frac{1}{10}(79+70+..............+74+74)$

$\large \bar{x} = \frac{740}{10} = 74$

​​$\large \therefore Variance = \frac{1}{10-1}\left [ (79-74)^{2}+(70-74)^{2}+................+(74-74)^{2} \right ]$

$\large \therefore Variance = \frac{68}{9}$

$\large \therefore Variance = 7.5556$

On rounding to two decimal places we get,

Variance = 7.56

The standard deviation is given as follows :

$\large s = \sqrt{ Variance }$

$\large s = \sqrt{ 7.5556 }$

$\large s = 2.749$

s = 2.749, Var = 7.55

Hence, second option is correct.