Question

Listed below are measurements of the “head injury criterion” (hic) for the following seven small cars tested in crashes by the National Highway Traffic Safety Administration: Chevrolet Aveo, Honda Civic, Volvo S40, VW Jetta, Hyundai Elantra, Kia Rio, and Kia Spectra. Higher numbers are associated with a higher risk of injury.

371     356     393    544    326     520    501

Range and Standard Deviation. Exercises each provide a set of numbers. In each case, find the range and standard deviation.

 

 

Answer 1

From the given information, the head injury criterion (hic) values 371, 356, 393, 544, 326, 520, and 501respectively for the given set of cars.

From the given information, maximum data value is 544 hic and minimum value is 326 hic. We know that range of the given set of sample values found as follows:

 

Range = (maximum data value) – (minimum data value)

             = 544 – 326

Range = 218 hic.

 

Therefore, the range of the given set of observations is 218 hic.

 

From the given information the sample size n = 7, Σx2 = 1342439, and Σx = 3011, We know that variance of given set of sample value found as follows:

 

Variance(s2) = Σ(x – x̅)2/(n – 1)

                       = n(Σx2) – (Σx)2/n(n – 1)

                       = 7(1342439) – (3011)2/7(7 – 1)

Variance(s2) = 7879.81 (hic)2.

 

Therefore, the variance of the given sample is 7879.8 (hic)2.

 

We know that standard deviation be the positive square root of the variance, that is

Standard deviation (s) = √variance (s2)

                                        = √7879.81

Standard deviation (s) = 88.77 hic.

 

Therefore, the standard deviation of the given sample is 88.77 hic.

 

The range for the given small cars is 218 hic, which is relatively large, so the head injury measurements are not about the same.

The range for the given small cars is 218 hic, which is relatively large, so the head injury measurements are not about the same.