MATH1725 Introduction to Statistics: Worked examples

Required percentage is
265.8
400
× 100 = 66.4%
Worked Example: Lectures 1–2
The Christmas cactus Zygocactus truncatus has branches made up of separate segments. For one
such cactus the number of segments in each branch were counted.
Number x of segments 1 2 3 4 5 6 7 8 9
Number of branches with x segments 3 0 6 7 8 18 8 0 2
Construct a cumulative frequency polygon to represent these data.
Answer: The data is discrete so cumulative frequency plot is a step function.
Number x of segments 1 2 3 4 5 6 7 8 9
Number of branches with ≤ x segments 3 3 9 16 24 42 50 50 52
Cumulative freq.
0 10 20 30 40 50 60
0 2 4 6 8 10
Number of segments
Worked Example: Lectures 1–2
The following data give one hundred measurement errors made during the mapping of the American
state of Massachusetts during the last century.
Error X (in minutes ′ of arc) (−4, −2] (−2,0] (0,+2] (+2,+4] (+4,+6]
Frequency 10 43 39 5 3
Show that the sample mean and sample standard deviation for these data are ¯x = −0.04 ′ and
s = 1.717 ′ respectively.
Answer:
Class Class frequency f Class mid-point x fx fx 2
−4< x ≤−2 10 −3 −30 90
−2< x ≤ 0 43 −1 −43 43
0< x ≤+2 39 +1 39 39
+2< x ≤+4 5 +3 15 45
+4< x ≤+6 3 +5 15 75
Totals n = 100 −4 292
2