Every corporation has a governing board of directors.The number of individuals on a board varies from onecorporation to another. One of the authors of the article“Does Optimal Corporate Board Size Exist? AnEmpirical Analysis” (J. of Applied Finance, 2010:57–69) provided the accompanying data on the numberof directors on each board in a random sample of 204corporations.No. directors: 4 5 6 7 8 9Frequency: 3 12 13 25 24 42No. directors: 10 11 12 13 14 15Frequency: 23 19 16 11 5 4 No. directors: 16 17 21 24 32Frequency: 1 3 1 1 1a. Construct a histogram of the data based on relativefrequencies and comment on any interestingfeatures.b. Construct a frequency distribution in which thelast row includes all boards with at least 18 directors.If this distribution had appeared in the citedarticle, would you be able to draw a histogram?Explain.c. What proportion of these corporations have at most10 directors?d. What proportion of these corporations have morethan 15 directors?
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Every corporation has a governing board of directors.
The number of individuals on a board varies from one
corporation to another. One of the authors of the article
“Does Optimal Corporate Board Size Exist? An
Empirical Analysis” (J. of Applied Finance, 2010:
57–69) provided the accompanying data on the number
of directors on each board in a random sample of 204
corporations.
No. directors: 4 5 6 7 8 9
Frequency: 3 12 13 25 24 42
No. directors: 10 11 12 13 14 15
Frequency: 23 19 16 11 5 4
No. directors: 16 17 21 24 32
Frequency: 1 3 1 1 1
a. Construct a histogram of the data based on relative
frequencies and comment on any interesting
features.
b. Construct a frequency distribution in which the
last row includes all boards with at least 18 directors.
If this distribution had appeared in the cited
article, would you be able to draw a histogram?
Explain.
c. What proportion of these corporations have at most
10 directors?
d. What proportion of these corporations have more
than 15 directors?
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