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2.1 Calculate the most appropriate measures of central tendency for each variable listed. Show all work. Explain your choices in each case. Discuss what each result means in real terms.

A. GNDR
B. TRAK
C. ADV
D. GPA

2.2 Calculate the most appropriate measures of dispersion for each variable listed. Show all work. Explain your choices in each case. Discuss what each result means in real terms.

A. TRAK
B. LIKE
C. STDY
D. GPA

[See the attached questions file.]

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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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