IQO: The Highway Loss Data Institute Collects Data

IQO The Highway Loss Data Institute Routinely Collects Data On Colli

The Highway Loss Data Institute routinely collects data on collision coverage claims. Collision coverage claims insures against physical damage to an insured individual’s vehicle. The data represents random collision coverage claims based on data obtained from the Highway Loss Data Institute for 2007 models. Find and interpret the first, second, and third quartiles for collision coverage claims. $6751 $9908 $3461 $21,147 $2332 $2336 $189 $1185 $370 $1414 $4668 $1953 $10,034 $735 $802 $618 $180 $1657 Quartile 1: _____ Quartile 2: _____ Quartile 3: _____ Interpretation (Explain):

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The collection and analysis of collision coverage claims data provide valuable insights into the distribution and frequency of physical damages incurred by insured vehicles. This data, gathered by the Highway Loss Data Institute for 2007 models, offers a snapshot of the financial impact of vehicle collisions on insurance providers and policyholders. A fundamental step in understanding this dataset involves calculating the first, second, and third quartiles, which summarize the distribution of claim amounts and facilitate interpretation of the data's spread and central tendency.

To begin, we organize the data into an ordered list. Sorting the data points from smallest to largest gives:

• 189, 370, 618, 735, 802, 1185, 1414, 1657, 180, 1953, 2332, 2336, 3461, 4668, 6751, 9908, 10034, 21147

Next, we calculate the quartiles. The median (second quartile, Q2) divides the data into two equal halves. Since we have 18 data points, the median is the average of the 9th and 10th values:

Median (Q2) = (180 + 1953) / 2 = 2133 / 2 = 1066.5

The first quartile (Q1) is the median of the lower half (first nine data points):

Lower half: 189, 370, 618, 735, 802, 1185, 1414, 1657, 180

Q1 is the median of these nine values, which is the 5th value:

Q1 = 802

The third quartile (Q3) is the median of the upper half (last nine data points):

Upper half: 1953, 2332, 2336, 3461, 4668, 6751, 9908, 10034, 21147

Q3 is the median of these nine values, which is the 5th value:

Q3 = 4668

Interpretation (Explain):

The first quartile (Q1) of $802 indicates that 25% of collision claims are at or below this amount, reflecting lower-cost claims involving minor damages or pettiness. The median (Q2) of approximately $1066.50 suggests that half of all claims are below this value, providing a center point of the dataset and highlighting that most claims involve relatively moderate damages. The third quartile (Q3) of $4668 indicates that 75% of claims are at or below this higher amount, representing more significant damages but still within the upper range of common claims.

The spread between Q1 and Q3 ($4668 - $802 = $3866) indicates a substantial variability in claim sizes, with some claims involving very high costs, especially considering the maximum claim of $21,147. The large difference between Q3 and the maximum suggests the presence of outliers or extremely high claims influencing the upper tail of the distribution. The data's median being closer to Q1 than Q3 highlights a right-skewed distribution, typical in insurance claims where most incidents involve moderate damages, but a few result in very high costs.

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