Probability & Statistics : Mean, Median and Histograms

9. The price-to-earnings (PE) ratio of a stock is the ratio of a stock's most recent price per share to the stock's earnings per share (averaged over a 12-month period). Listed below are the PE ratios for 40 randomly selected securities traded on the New York Stock Exchange (NYSE) on Wednesday, August 24, 2005.

Stock PE Ratio
1 ALLGWASTE 25
2 AZISTA 22
3 CIMAREXENGY 10
4 DEVRY 47
5 DLRGENL 18
6 ENPRO 15
7 GENESCO 18
8 GILDAN 27
9 GUESS 26
10 HEAD 33
11 HOSPIRA 23
12 IBM 17
13 INCO 10
14 JEFFPILOT 12
15 K2 25
16 KINDRED 10
17 LEAR 15
18 MANPOWER 17
19 MESTEK 4
20 MIHOMES 10
21 MYLANLABS 30
22 NUCOR 6
23 ONEOK 14
24 PROQUEST 22
25 PULTE 9
26 RUDDICK 16
27 SIRVA 40
28 STEINWAY 15
29 TESORO 13
30 TORCHMARK 12
31 TORO 16
32 UNITCP 18
33 VARIANMED 27
34 WALLGREEN 31
35 WELLCHOICE 22
36 WELLPOINT 23
37 WILEYA 32
38 XEROX 13
39 YANKEECANDL 16
40 ZIMMER 29
(a) Give the mean ( ), median, variance (s2), and standard deviation (s) for this data sample.

(b) For this data sample, approximately what percentage of the data lies within one standard deviation of the mean?

(c) Create a Histogram for this data. (Use about 6 classes)

10. Mary tosses a coin three times and then John does the same.
a. Find the probability that Mary obtains exactly one Head.
b. Find the probability that Mary obtains exactly one Head and so does John. [Hint: We assume that Mary's tosses are completely independent from John's.]
c. Find the probability that each of them obtain exactly 2 Heads. [Hint: This means find the probability that Mary obtains 2 heads and so does John.]
d. Find the probability that each of them obtains no Heads.
e. Find the probability that they obtain the same number of Heads.
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