STA101: Introduction to Statistics
Assignment 2
Marks: 30
1. The following table provides a number of pieces of information on a variety of different
Source: https://www.fueleconomy.gov
[4]
Model
Engine
size
Cylinders
Transmission
Number
of gears
Fuel
Vehicle
City
Hwy
Model
Class
small
SUV
MPG
MPG
Year
19
28
2010
ACURA RDX
3.5
6
Automatic
6
Gasoline
HYUNDAI
Sonata
1.6
4
Manual
7
Gasoline
large car
28
38
2015
1.6
4
Manual
5
Gasoline
Small car
28
36
2006
DODGE
Challenger
6.4
8
Automatic
8
Gasoline
midsize
car
15
25
2010
BMW X5
xDrive35i
3
6
Automatic
8
Gasoline
standard
SUV
18
24
2013
HONDA
Accord
3.5
6
Automatic
6
Gasoline
midsize
car
21
32
2014
LAND
ROVER Range
Rover
3
6
Automatic
8
Diesel
standard
SUV
22
29
2008
BENTLEY
Mulsanne
6.8
8
Automatic
8
Gasoline
midsize
car
11
18
2012
MAZDA CX-5
2.5
4
Automatic
6
Gasoline
small
SUV
24
30
2013
PORSCHE
Cayman GTS
3.4
6
Manual
6
Gasoline
small car
19
26
2015
Ford Fiesta
a) What is the mean, median and mode of City MPG?
[0.5+1+0.5]
b) What is the mean, median and mode of Highway MPG?
[0.5+1+0.5]
STA101 (Introduction to Statistics) _Assignment 2_Spring 2023
2. The number of Tesla, Inc. employees who will be selected for various salary bands in 2022 is
demonstrated in the following table:
[5]
Wages ($)
40k – 50k
50k – 60k
60k – 70k
70k – 80k
80k – 90k
No. of Employees
Y+8
24+√49
19
√121 + Y
√225
Here, Y is the last digit of your student ID (i.e., 20100012, 21123415, etc.). Suppose your ID
is 20100012, then the 2nd last row (70k-80k) will be √121+2 = 13]. Estimate the following:
a) Find the Range of wages ($) and complete the frequency distribution table.
b) Find:
i. Mean
ii. Median
iii. Mode
[0.5+0.5]
[1]
[1.5]
[1.5]
3. The stock price of AAA Cable Company for the 24 trading days are in the following table
below:
[8.5]
92 87 72 65 86 77 81 69
88 77 62 65 57 47 31 69
52 54 68 63 42 45 49 58
For the given information
a)
b)
c)
d)
e)
f)
g)
Construct Stem and leaf plot
Determine 𝑄1 , 𝑄2 𝑎𝑛𝑑 𝑄3 Quartiles
Determine 𝐷5 𝑎𝑛𝑑 𝐷8 deciles
Determine 𝑃30 , 𝑃80 𝑎𝑛𝑑 𝑃67 Percentiles
Draw Box and whiskers plot
Determine IQR
Calculate the coefficient of skewness and comment on the shape distribution
STA101 (Introduction to Statistics) _Assignment 2_Spring 2023
[1]
[1.5]
[1]
[1.5]
[1.5]
[0.5]
[1.5]
4. A study on a range of automotive lubricants reported the following data on oxidationinduction time (min) for various commercial oils:
[12.5]
Sample 1:
87
103
130
160
180
195
132
145
211
105
145
153
152
138
87
99
93
119
129
Sample 2:
99
102
201
209
110
103
33
66
56
84
112
75
130
107
111
202
124
59
a) What are the sample size of the sample 1 & 2 individually?
155
[0.5]
b) Compute the sample mean, variance, and standard deviation for sample 1.
[1+2.5+0.5]
c) Compute the sample mean, variance, and standard deviation for sample 2.
[1+2.5+0.5]
d) Compute the Coefficient of variation for sample 1.
[0.5]
e) Compute the Coefficient of variation for sample 2.
[0.5]
f) Which measure one should consider to compare the performance/consistency among the
sample data? And why?
[2]
g) For which sample of commercial oils, the relative variability of oxidation-induction time is
higher?
STA101 (Introduction to Statistics) _Assignment 2_Spring 2023
[1]