Data Distributions Analysis: Statistics Assignment, [Course Name]

This statistics assignment analyzes the properties of probability distributions using real-world data from Facebook's stock prices. The assignment involves calculating descriptive statistics, including mean, median, and quartiles, and visualizing data through box plots. The student determines the distribution's skewness and explores the normal probability distribution. Part B focuses on calculating probabilities related to stock price changes using a given sample, while Part C examines confidence intervals for the mean daily change. Excel is used extensively for calculations, with interpretations provided for each analysis. The assignment covers key statistical concepts such as descriptive statistics, probability distributions, and confidence intervals, applying them to a practical scenario of stock price fluctuations.

PROBABILITY AND STATISTICS
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PART A
Question 1
Properties probability distribution
a. Data is attached in excel spreadsheet.
Company: Facebook
Time period: April 2, 2019 to May 31, 2019
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b. Daily change in closing stock prices has been computed in Excel and the final result is
pasted below.
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Formula used for computation of daily change is shown below.
Daily change= (Closing Price – Opening Price)
c. Descriptive statistics has been computed through the use of Excel.
d. First and third quartile and five number summary for the daily price change for the given
four week period for Facebook stock has been computed using Excel.
Five Number Summary
e. The box and whisker plot has been obtained through the use of the above five number
summary for the daily change besides the use of Excel.
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f. It is evident from the above box plot that the distribution is not symmetric. From the
descriptive statistics corresponding to the daily change, it is evident that the median (-
0.10) is lesser than the mean (0.15) and hence it can be concluded that there is a right
skew in the distribution of daily change in Facebook stock prices over the 4week period
under consideration.
Question 2
Normal probability distribution
a. It is apparent from above the descriptive statistics the underlying distribution is non-
normal considering that the mean and median do not coincide. Also, there is presence of
skew which should be zero for normal distribution. Besides, kurtosis is ot equal to 3.
PART B
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The requisite computations have been performed in Excel using the template provided. The
results are illustrated and the interpretation provided below.
Question 1
Decrease of 0.5 points or more (X<= -0.5)
Using the given sample, P(X<= -0.5) = 0.01625
Question 2
Increase of more than 0.5 point (X > 0.5)
Using the given sample, P(X> 0.5) = 0.1248
Question 3
Decrease of 1 point or more (X<= -1)
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Using the given sample, P(X<= -1) = 0.0001
Question 4
Using the given sample, P(X>1) = 0.1587
Question 5
Based on the results of Q1-Q4, it may be concluded that the likelihood of any change would
be less only.
PART C
Input variables
95% confidence interval
From the above output, it can be concluded with 95% confidence that mean daily change
would lie between -0.446 to 0.746.
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