Reading 7: Statistical Concepts and Market Returns-LOS f 习题 2011, following, interpret, center, median

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Session 2: Quantitative Methods: Basic Concepts
Reading 7: Statistical Concepts and Market Returns

LOS f: Describe, calculate, and interpret quartiles, quintiles, deciles, and percentiles.

 

 

What are the median and the third quintile of the following data points, respectively?

9.2%, 10.1%, 11.5%, 11.9%, 12.2%, 12.8%, 13.1%, 13.6%, 13.9%, 14.2%, 14.8%, 14.9%, 15.4%

A) 13.1%; 13.6%.

B) 13.1%; 13.7%.

C) 12.8%; 13.6%.

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The median is the midpoint of the data points. In this case there are 13 data points and the midpoint is the 7^th term.

The formula for determining quantiles is: L_y = (n + 1)(y) / (100). Here, we are looking for the third quintile (60% of the observations lie below) and the formula is: (14)(60) / (100) = 8.4. The third quintile falls between 13.6% and 13.9%, the 8^th and 9^th numbers from the left. Since L is not a whole number, we interpolate as: 0.136 + (0.40)(0.139 ? 0.136) = 0.1372, or 13.7%.

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What does it mean to say that an observation is at the sixty-fifth percentile?

A) 65% of all the observations are above that observation.

B) The observation falls within the 65th of 100 intervals.

C) 65% of all the observations are below that observation.

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If the observation falls at the sixty-fifth percentile, 65% of all the observations fall below that observation.

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Consider the following set of stock returns: 12%, 23%, 27%, 10%, 7%, 20%,15%. The third quartile is:

A) 21.5%.

B) 23%.

C) 20.0%.

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The third quartile is calculated as: L_y = (7 + 1) (75/100) = 6. When we order the observations in ascending order: 7%, 10%, 12%, 15%, 20%, 23%, 27%, “23%” is the sixth observation from the left.

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The following data points are observed returns. 

4.2%, 6.8%, 7.0%, 10.9%, 11.6%, 14.4%, 17.0%, 19.0%, 22.5%, 28.1%

What return lies at the seventh decile (70% of returns lie below this return)?

A) 17.0%.

B) 19.0%.

C) 18.4%.

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The formula for the seventh decile is L_y = (n + 1)(7 / 10) = 7.70 or between the seventh and eighth return from the left. The seventh return is 17%, while the eighth return is 19%. Interpolating, we find that the seventh decile is 17% + 0.7(19% – 17%) = 18.4%.