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Question:
The following stem and leaf display represents the final exam scores for a class of 25 literature students:
[Please refer to the attachment for the figure]

a. Convert the stem and leaf display into a frequency distribution, using a lower limit for the first class of 20 and a class width of 15. Complete the following frequency distribution table.

b. Using the frequency distribution table, calculate the mean exam score of the students.

c. Using the frequency distribution table, calculate the standard deviation of exam scores.

d. Construct a cumulative percentage of the given of examination scores

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Sufficiency and Order Statistics

Let Y1<Y2<...<Yn be the order statistics of a random sample of size n from the uniform distribution over the closed interval [-theta, theta ]
having pdf f(x; theta ) = (1/2(theta))I[-theta , theta ](x).

Argue that the mle of theta; equals theta;hat= max(-Y1, Yn).
Demonstrate that the mle theta;hat is a sufficient statistic for theta;.
Define at least two ancillary statistics for this distribution

See attachment for better symbol representation.

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