Car Insurance Brokerage Services Analysis

FOUNDATION
SKILLS IN DATA
ANALYSIS
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Executive Summary
The objective of the underlying report is to outline the findings derived from the analysis of
the sample data in wake of the queries raised by Paul Anderson through his memorandum.
The average savings for the sample is faithfully presented based on median rather than mean
on account of highly skewed nature of the savings variable. There is presence of outliers
especially on the higher end which had led to high variation in customer savings. The
insurance brokers performance is not the same as there are sizable differences with regards to
mean savings and also the variation in the same. The satisfaction ratings by sample customers
indicate high satisfaction levels but these are impacted by both living area and gender of the
customer. The car value and car insurance premium has indicated a strong positive linear
relationship while the relationship with other variables does not seem significant. There is
95% chance that the mean savings for all customers would lie in the range ($ 198.71,
$261.74). The mean proportion of all the customers that would be worse off availing broker
services are estimated to lie in the range (14.24%, 21.76%). With 95% certainty, it may be
stated that the average savings realised at present are not significantly different from that
which the customers realised on average couple of year ago. The sample data does not lend
support to the claim that less than 40% of all males tend to avail the broker services for car
insurance. If the researcher wants to choose a sample for which both the above objectives
may be achieved, then such a sample must contain atleast 158 subjects.

Title: Car Insurance Brokerage Services Analysis
Introduction
The given report aims to highlight the key findings with regards to the statistical analysis for
the sample data which comprises of the purchase data of 400 randomly selected customers.
The statistical analysis has been conducted for providing response to the questions that Paul
Ansderson had raised in his memorandum. The sample data has been used to present the
summary along with indicating the characteristics of the population in relation to various
aspects of car insurance brokerage services. The questions raised by Paul have been
chronologically addressed in the given report.
Consumers’ savings summary
The sample of 400 customers highlights that the mean annual savings with regards to car
insurance premium is $ 230.24. Further, the distribution of the sample data savings is such
that it indicatives high dispersion. Besides, some customers have derived savings in premium
which are quite abnormal (very large) which has lead to the savings amount being quite
skewed for the sample data. These large values of savings tend to distort the mean savings
and hence a preferred option would be median savings (Eriksson and Kovalainen, 2015). This
median value of sample savings is $ 116.50 and indicates that 50% of the sample customers
realised an insurance premium savings which is less than or equal to $ 116.50. It is
noteworthy that there are customers who have realised negative savings and thereby ended up
paying extra when using brokerage services. On the contrary, there are others included in the
sample who have realised savings to the extent of $ 1.956. Besides, 25% of the customers
had a savings which was less than equal to $ 12 which implies only nominal returns. Thus, it
would be fair to conclude that three fourths of the sample customers saved more than $ 12
using brokerage services which indicates its utility for customers (Flick, 2015).
Individual insurance brokers performance comparison
The sample customer savings based on the insurance brokers does indicate that the
performance of insurance brokers is not the same. If the median savings of the various
insurance brokers sample customers is compared, it becomes apparent that the lowest median
savings is realised by Broker C ($ 94.50). In comparison, for Broker D, the sample customers
realised a median cost savings of $134.50 which is significantly higher. Besides, consistency
of the insurance brokers has also been measured based on the underlying variation in savings