MEASURES OF SPREAD
(RANGE, VARIANCE, STANDARD DEVIATION)
Measures of spread describe how the values in a set of data are distributed.
(describe how spread out the values are from the mean)
range:
the difference between
the greatest and the
least values
variance:
the mean of the squares of
the deviations from the mean
standard deviation:
Example 1:
 = var iance
Sabrina’s monthly gasoline expenses, in dollars, are shown.
61
83
77
88
67
71
65
72
67
84
90
80
Calculate the range, mean, variance, and standard deviation.
a)
range
b)
mean
c)
variance
d)
standard deviation
xi
( x i  x)
( x i  x )2
61
83
77
88
67
71
65
72
67
84
90
80
Unit 8 Lesson 5
Page 1 of 2
Example2:
A company needs bolts for its heavy machinery. The company must
choose between two bolt manufacturers: CanInco and QualiTek. Both
manufacturers produce bolts with a mean length of 72mm. According
to quality control records, bolts from CanInco have a standard deviation
of 2mm while bolts from QualiTek have a standard deviation of 0.1mm.
Which manufacturer should the company choose? Explain.
In summary, range, variance, and standard deviation
are values that can be used to measure the spread
in a set of data. The greater these values,
the greater the spread of the data values.
Homework: p.145–146 #2–8, 10
Unit 8 Lesson 5
Page 2 of 2