Question

An insurance company crashed four cars in succession at 5 miles per hour, and the cost of repair for each of the four crashes was as follows: $430, $454, $415, and $233. Compute the following statistics for the cost of repair:

a) Range
b) Sample Variance
c) Sample Standard Deviation

Answer 1

The range of the repair costs is $221, the sample variance is 10,258, and the sample standard deviation is approximately $101.28.

Step-by-step explanation:

The range, sample variance, and sample standard deviation are measures of dispersion that indicate the spread of data points in a data set.

To calculate the range, subtract the smallest value from the largest value in the dataset.
Range = Max value - Min value
Range = $454 - $233
Range = $221

To compute the sample variance, follow these steps:
1. Find the mean (average) of the dataset.
Mean = ($430 + $454 + $415 + $233) / 4
Mean = $1,532 / 4
Mean = $383
2. Subtract the mean from each data point and square the result.
3. Sum up all the squared differences.
4. Divide by the number of data points minus one (n - 1) to get the sample variance.

Sample Variance calculation:
Sum of squared deviations = ($430 - $383)^2 + ($454 - $383)^2 + ($415 - $383)^2 + ($233 - $383)^2
Sum of squared deviations = 2,209 + 5,041 + 1,024 + 22,500
Sum of squared deviations = 30,774
Sample Variance = 30,774 / (4 - 1)
Sample Variance = 30,774 / 3
Sample Variance = 10,258

The sample standard deviation is the square root of the sample variance.
Sample Standard Deviation = √(10,258)
Sample Standard Deviation ≈ $101.28