Business Statistics
Home assignment #2
Submit a hard copy of your solution at the beginning of the lecture.
1. A Hyundai Motor Company builds several engine types for their i30 class vehicles.
One of them is 1.6 liter GDI engine with 99kW power. However, it is very difficult
to build each engine with precisely 99kW power. If the engine is underpowered, two
problems arise. First, customers may not be satis ed with the car performance as
the engine is one of the car essential components. Second, the company may be in
violation of the truth-in-labeling laws. In this example, Hyundai Motor Company
in fact indicates that, on average, their engine power is 99kW. If the average power
of the engine exceeds the advertised power, the company is giving away product (to
build stronger engine is more expensive). However, getting an exact engine power is
problematic because it depends on vast amount of components and precision of their
processing. The attached le provides a table with the engine power of a sample of
50 engines produced during certain day in the same factory.
(a) Compute the arithmetic mean and median.
(b) Compute the rst quartile and third quartile.
(c) Compute the minimum maximum range, interquartile range, variance, standard
deviation, and coefficient of variation.
(d) Construct a boxplot. Are the data skewed? If so, how?
(e) Interpret the measures of central tendency within the context of this problem.
Why should the company building car engines be concerned about the central
tendency?
(f) Interpret the measures of variation within the context of this problem. Why
should the company building car engines be concerned about variation?
2. Use the delivery dataset we are working with since the rst lecture.
(a) Find all descriptive statistics that we have discussed in class for the DeliveryFee
of private customers. Construct the boxplot of this variable and comment on
the shape of its distribution.
(b) Exclude outliers among DeliveryFee of private customers. Reconstruct the box-plot. How did the outliers exclusion helped you to better describe the distribu-tion?
(c) Find the coefficient of correlation between DeliveryFee and Weigh among the
private customers. Plot the scatterplot between these two variables. Comment
your results in the context of the delivery rm case study.
Engine Power
99.3
99.5
99.7
99.7
100.2
100.9
99.8
99.2
100.6
100.7
100.4
100.9
100.0
100.0
99.6
100.7
100.4
99.5
100.5
100.9
99.9
100.3
99.2
99.5
100.0
99.1
99.2
99.3
99.7
99.8
100.9
99.0
100.5
99.4
99.3
99.9
99.3
99.3
99.6
99.2
100.7
99.8
99.8
100.2
100.3
100.9
99.6
100.7
100.7
99.7
PLACE THIS ORDER OR A SIMILAR ORDER WITH US TODAY AND GET AN AMAZING DISCOUNT 🙂