5.10)
anything where the numbers are further away from the mean will do. For example, 15, 30, 40, 55, as long as the average of the numbers is still 35.
5.12)
a.) A boxplot.
b.) There was between 50% and 75% that did better than that person.
c.) a 780 was needed.
5.20)
a.) Both ranges for plot 1 and plot 2 are equal.
b.) Both plot 1 and plot 2 are symmetric about 0, so the mean is the same.
c.) Plot 1 has a larger std dev than plot 2.
d.) Plot 1: Range = 2 � (-2) = 4; Mean = 0; Std Dev = 1.49
Plot 2: Range = 4; Mean = 0; Std Dev = 1.15
5.28)
a.) Z = (45 � 63)/12 = -1.5
b.) X = � + z(?) = 30 + (-1)5 = 25
c.) 2 � (-2) = 4. They are four std deviations away from each other.
5.31)
b.) The mean would be higher than the median because this is a skewed to the right distribution.
5.32)
a.)
i.) the sample median is 10.
ii.) the sample mean is 10.
iii.) the range is 13 � 7 = 6.
iv.) the sample std deviation is 2. The variance is four.
v.) the 80th percentile is 11.
b.) The range and the sample standard deviation, s.
5.38)
a.) About 25%.
b.) About 270%.
c.) 100 aircraft.
5.55)
a.) Station 2.
b.) can�t tell.
c.)
i.) mean = 9.67; std. deviation = 3.142
ii.) min = 3, Q1 = 9; Q2 = 10.5; Q3 = 11; max= 15
iii.) IQR = 2; step # = 3; 3,5 and 15 are all outliers.
iv.)
_________
o o |______|__|------| o
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
v.) The std deviation should be the same, as all the pts are still kept the same distance apart. The sample mean is the only thing that changes, and it is now 10.67.