Mark Hansen, Fall 2009
CE93 Homework 2 – Solution
1. Sample median and mean values.
> median(x), mean(x), median(y), mean(y)
Data
Median
Mean
Density
2445
2444.9
Strength
60.10
60.14
These measures fall in the central regions of the corresponding normalized frequency diagrams
as shown in the following figures.
Mean=median=2445
mean=median=60.1
2. Range, IQR, Mean absolute deviations,
d
, the sample (unbiased) variance,
s
2 , the sample
(unbiased) standard deviations,
s
and the sample c.o.v.’s
d
ˆ .
>> range(x), IQR(x), mad(x), var(x), std(x), std(x)/mean(x), std(x,1)
>> range(y), IQR(y), mad(y), var(y), std(y), std(y)/mean(y), std(y,1)
Data
Range
IQR
d
s
2
s
g
G
s normalized by N
Density
77
19
12.2
255.8
16.0
0.0065
15.8
Strength
19.6
6.55
3.84
25.15
5.01
0.0834
4.95
The estimate of the standard deviation when normalized by
N
is slightly smaller than the
unbiased estimate.
The strength data has higher dispersion since it has a larger sample c.o.v.