MBF3C
Name:
BLM 5.7.1
Standard Deviation
Date:
1. True or False?
The standard deviation cannot be negative.
2.
Calculate the range and standard deviation of each.
a) 4, 8, 6, 3, 12, 9, 7, 6
b) 35, 38, 40, 43, 46, 23, 38
c) 2.4, 4.3, 6.5, 1.1, 8.9, 3.6, 7.2, 9.6
d) 4.55, 3.23, 6.78, 3.54, 5.54, 6.78
3.
The machine packaging cookies has been considered defective.
The packages are labelled as
containing 150g. A sample of 15 packages was selected and the masses are given.
145,
151,
152,
150,
147,
152,
149,
148,
153,
150,
146,
152,
148,
149,
151
a)
Calculate the mean.
b)
If any packages are more than 2.2g from the mean, the package is not sold.
How
many are defective?
c)
Should the machine be fixed?
4.
A group of student landscapers are to keep track of their own weekly hours.
They are listed
below.
44,
52,
43,
39,
42,
41,
38,
43,
46,
45,
44, 39,
40,
42,
45
a)
Find the range.
Is this a useful tool for representing this data?
b)
Find the mean.
c)
Find the standard deviation.
d)
What can be said about the entry of 52 hours/week?
e)
Calculate the standard deviation again without the 52 hours/week entry.
5.
The sale prices of the last 10 homes sold in 1985 were: $198 000, $185 000, $205 200,
$225 300, $206 700, $201 850, $200 000, $189 000, $192 100, $200 400.
a)
What is the average sale price?
b)
What is the standard deviation?
c)
Do you think that a price of $240 000 would be considered unusual? Why or why not?
6.
The sales price of the last 10 homes sold in 2005 were: $345 500, $467 800, $289 000,
$675 000, $398 500, $243 000, $899 950, $453 000, $239 000, $256 000.
a) What is the average sales price?
b) What is the standard deviation?
c) Which year was more consistent?
How do you know?
Solutions
1.
true
2.
a)
range = 9; s.d. = 2.85
b)
range = 23; s.d. = 7.37
c)
range = 8.5; s.d. = 3.08
d)
range = 3.55; s.d. = 1.55
3.
a)
149.5
b)
7
4. a)
14; yes, to ensure that students are being honest
when recording the number of hours worked
b)
42.9
c)
3.50
d)
answers may vary; for example:
over-inflated
e)
2.52
5.
a)
$200 355
b)
11 189.04
c)
yes, based on the standard deviation, it
would be an extremely high value
6. a)
$426 675
b)
214 078.1
c)
1985; smaller range of values