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MATH 2565
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Jagmohan Chawla
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# PPS2_Solution_.doc

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York University

Mathematics and Statistics

MATH 2565

Jagmohan Chawla

Winter

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Problem4.13
a) The mean price of the electric smoothtop ranges is
$1001.50.
b) In order to find the median and the quartiles, the
list must be ordered.
565 750 850 900 1000 1050 1050 1200 1250 1400
The median price of the electric smoothtop ranges is
$1025.
Quartile 1 = $850 and Quartile 3 = $1200.
c) The range of the distribution of prices is Max – Min =
$1400 – $565 = $835.
The IQR = Q3 – Q1 = $1200 – $850 = $350.
Problem4.15
a) As long as the boss’s true salary of $200 000 is still above
the median, the median will be correct. The mean will be
too large, since the total of all the salaries will decrease
by $2 000 000 – $200 000 = $1 800 000, once the mistake
is corrected.
b) The range will likely be too large. The boss’s salary
is probably the maximum, and a lower maximum would
lead to a smaller range. The IQR will likely be unaffected,
since the new maximum has no effect on the quartiles.
The standard deviation will be too large, because the $2
000 000 salary will have a large squared deviation from
the mean.
Problem 4.17
a) Set 2 has the greater standard deviation. Both sets have
the same mean (6), but set two has values that are
generally farther away from the mean.
SD(Set 1) = 2.24 SD(Set 2) = 3.16
b) Set 2 has the greater standard deviation. Both sets
have the same mean (15), maximum (20), and minimum
(10), but 11 and 19 are farther from the mean than 14
and 16.
SD(Set 1) = 3.61 SD(Set 2) = 4.53
c) The standard deviations are the same. Set 2 is simply Set
1 + 80. Although the measures of centre and position
change, the spread is exactly the same.
SD(Set 1) = 4.24 SD(Set 2) = 4.24
Problem 4.19
1200+700+6(400)+4(500))
a) The mean salary is 12 = 525
The median salary is the middle of the ordered list:
400 400 400 400 400 400 500 500 500 500 700 1200 The median is $450.
b) Only two employees, the supervisor and the
inventory manager, earn more than the mean wage.
c) The median better describes the wage of the typical
worker. The mean is affected by the two higher salaries.
d) The IQR is the better measure of spread for the
payroll distribution. The standard deviation and the

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