MAT 1100 Quantitative Reasoning - Module 4 Lesson 4 Assignment 1

This document provides solutions to problems related to finding the range and standard deviation for given data sets. It also includes explanations on the impact of replacing a data point on the range and standard deviation, and the preference of standard deviation over range as a measure of variation.

MAT 1100 Quantitative Reasoning Module 4 Lesson 4 Assignment 1
Student Name:
Find the range for the set of data given in problems 1) , 2) and 3).
1)
Range = maximum value – minimum value
607- 117 = 490
2)
Range = maximum value – minimum value
35- 15 = 20
3)
Range = maximum value – minimum value
74 - 70 = 4
Find the standard deviation from problems 4) to 5). Round to one more place than the data.
4) 14, 14, 10, 7, 14, 14, 13, 19, 15, 15
standard deviation= √ ∑ ( x−μ ) 2
n
x x-μ (x-μ)^2
14 0.5 0.25
14 0.5 0.25
10 -3.5 12.25
7 -6.5 42.25
14 0.5 0.25
14 0.5 0.25
13 -0.5 0.25
19 5.5 30.25
15 1.5 2.25
15 1.5 2.25

MAT 1100 Quantitative Reasoning Module 4 Lesson 4 Assignment 1
90.5
mean 13.5
standard deviation= √ 90.5
10 =3.003
5) 18.1, 10.5, 32.3, 36.7, 17.0, 17.3
x x-μ (x-μ)^2
18.1 -4.88 23.8144
10.5 -12.48
155.750
4
32.3 9.32 86.8624
36.7 13.72
188.238
4
17.3 -5.68 32.2624
486.928
mean 22.98
standard deviation= √ 486.93
5 =9.87
Choose the one alternative that best completes the statement or answers the question.
Find the standard deviation for the given data. Round your final answer to one more decimal place
than that used for the observations
6) 74, 40, 82, 75, 70, 25 90, 57, 29
A) 22.4 B) 23.7 C) 7.5 D) 25.4
7) The manager of a small dry cleaner employs six people. As part of their personnel file, she asked each one
to record to the nearest one-tenth of a mile the distance they travel one way from home to work. The six
distances (in miles) are listed below.
23.3 13.2 27.7 33.3 21.3 12.9
A) 3213.4 mi B) 30.5 mi C) 2890.8 mi D) 8.03 mi
8) The manager of an electrical supply store measured the diameters of the rolls of wire in the inventory. The
diameters of the rolls (in m) are listed below.

MAT 1100 Quantitative Reasoning Module 4 Lesson 4 Assignment 1
0.239 0.559 0.259 0.338 0.111 0.345 0.396
A) 0.338 mm B) 0.8391 mm C) 0.1401 mm D) 0.7213 mm
Provide an appropriate response.
9) The range and standard deviation of the data set below are 35 and 12.47, respectively.
5, 24, 25, 26, 40
a) If the 26 is replaced with 39, how will this affect the range?
The range will not be affected
b) How will this affect the standard deviation?
The standard deviation increases since 39 is above the mean of the data.
c) Use your answers to explain why the standard deviation is preferable to the range as a measure of
variation.
Standard deviation is preferred to range since range only gives the general spread of the data from the
smallest to the largest while standard deviation gives the spread of each data point with respect to the mean.
10) Do you think it is possible to find two data sets such that the first data set has a smaller range but a larger
standard deviation than the second set?
a) If so, give an example of two such data sets.
b) If it is not possible, explain why not.
It is not possible since the wider the range, the more spread the data hence the greater the standard deviation.