2) The distance that a signal can travel along an internet optical cable before

Question

2) The distance that a signal can travel along an internet optical cable before falling below an
unrecognizable level is being studied. Sixteen tests are performed with the following results
(in km), which have been ordered from smallest to largest:
73.6, 86.3, 86.5, 91.3, 91.5, 93.7, 98.3, 100.7,
101.1, 106.4, 110.9, 113.2, 114.0, 115.3, 125.3, 139.4
a) Compute the values of the sample mean and the sample median.
b) By how much could the smallest sample observation be increased without affecting the
value of the sample median?
c) By how much could the smallest sample observation be increased without affecting the
value of the sample mean?
d) If you had to express the “design” length for this internet optical cable, to avoid becoming
unrecognizable, what length would you suggest? Discuss briefly.

Explanation / Answer

2.

Given sample data,

73.6, 86.3, 86.5, 91.3, 91.5, 93.7, 98.3, 100.7,

101.1, 106.4, 110.9, 113.2, 114.0, 115.3, 125.3, 139.4

a)

sample mean = (sum of number of observations)/number of observations

=(73.6+86.3+86.5+91.3+91.5+93.7+98.3+100.7+101.1+106.4+110.9+113.2+114.0+115.3+125.3+139.4)/16

= 102.9688

sample median,

when n=16 observations it is a n even number so that sample median is average of middle of two terms

sample median = (100.7+101.1)/2=100.9

b)

smallest observation(73.6) is increased without affecting sample median(100.9) so that the value increse is 27.3

c)

smallest sample observation be increased without affecting the

value of the sample mean that is 29.3688

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.