NYSE Statistical Data Measures

New York Stock Exchange

Exercise in

Central Tendency and Conditional Probability Measures

of Stock Market Prices

This assignment concerns the application of certain common statistical measures of data pertaining to the movement of stock prices. Source data for this exercise are the opening and closing prices for Barnes & Noble, Inc. (traded as BKS) and the opening and closing prices indexed under the Dow Jones Industrial Average (DJIA), along with calculated changes in these price movements, for the dates August 6-10, 2007. The statistical measures of note are three measures of central tendency – the mean, median, and mode – and, one concept of the likelihood of a particular outcome or event – **conditional** probability. Each of these fundamental measures is capable of yielding a significant indicator of performance of a stock price, though not necessarily in isolation of other data analysis.

I have created a spreadsheet that incorporates the BKS data with opening and closing DJIA prices for the same dates. In addition, this table also includes calculated change in the daily prices. The source of the DJIA OPEN and CLOSE figures was the Wall Street Journal newspaper’s Money & Investing Section C for each day’s reported activity.

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DATE

DJIA

BKS

OPEN

CLOSE

CHANGE

OPEN

CLOSE

CHANGE

VOLUME

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8/6/2007

13181.91

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13468.78

286.87

33.18

33.19

0.01

1,239,200

8/7/2007

13468.78

13504.30

35.52

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32.93

32.69

-0.24

1,671,300

8/8/2007

**13504**.30

13657.86

153.56

32.93

32.23

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-0.70

2,009,300

8/9/2007

13657.86

13270.68

-387.18

31.47

31.36

-0.11

2,449,400

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8/10/2007

13270.68

13239.54

-31.14

31.20

32.85

1.65

2,192,800

D E G

For expediency and clarification, the BKS data columns in this table will be designated as

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follows for the first part of the exercise in this assignment: BKS OPEN, denoted by column label D; BKS CLOSE, denoted by column label E; and, BKS CHANGE, denoted by column label G.

With these designations established, the first of the two (2) sets of questions posed for this essay will be answered:

(1) The possibility – or, impossibility – of deriving the mean, mode and median for BKS

OPEN, CLOSE , and VOLUME data (in columns D, E and G) ~ The mean (or, average), median and mode can be computed for the BKS OPEN series of data. Likewise, the mean and median can be computed for both the BKS CLOSE series of data and for the BKS VOLUME series of data. The mean simply expresses the average of the set of values in a given series as in columns D, E and G – the sum of each column of numbers divided by the sheer number of times (days) reported or observed. Deriving the median requires that the set of numbers in each column first be arranged in either ascending or descending order, in order to determine the value in the physical middle of the stream of figures. The mode can only be expressed if there is at least one value in a set of data that has greatest frequency over others in that set. Therefore, only column D has such instance among the BKS data sets provided. Consequently, the mode cannot be expressed for either the BKS CLOSE series of data or the BKS VOLUME **series** of data. Each value in the respective series under columns E and G occurs with equal frequency; hence, there is no mode in either of those sets of data.

(2) Computation of the conditional *probability* that the BKS stock price will __increase__ given that the Dow Jones Industrial Average (DJIA) has increased ~ As they are two independent events, the probability for the BKS stock price increase and that for the DJIA increase are calculated separately first (a), and then the ultimate result (b) is derived from the product of their probabilities.

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Designating X for the number of times (i.e., days) when the BKS stock price increased, and Y for the number of times (days) when the DJIA increased, out of the total number of times (days) for which data was collected:

(a) P(X) = 2 / 5 = .4 P(Y) = 3 / 5 = .6

(b) P(X|Y) = P(X∩Y) = P(X) * P(Y) = .4 * .6 = .24

Hence, the probability that the BKS stock price will increase if the DJIA increases, for the data provided, is 24 / 100, or .24 (24%).

References

http://library.thinkquest.org/

ThinkQuest (October 2003). In **English** and Dutch. Coaches Carol Calderwood, Dirk-an van der Poppe. Schools Institut Teknologi Bandung, Bandung, West Java, Indonesia; Newcastle High School, Newcastle, NSW, Australia; Jacobus Fruytier Scholengemeenschap, Apeldoorn, Gelderland, Netherlands. Quick online elementary reference consulted regarding the three central tendency measures, and particularly for computation of the conditional probability, and as well for information needed to cite this online source in the bibliography.

Order #31283953. Barnes & Noble, Inc. data sets.

McKay, Peter A. and Browning, E.S. (August 7-11, 2007). The Wall Street Journal. Money

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& Investing Section C. Dow Jones Industrial Average data. New York: Dow Jones &

Company.

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