Reading 7: Statistical Concepts and Market Returns-LOS f习题 2010, following, interpret, center, median

bmaggie

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) 12.8%; 13.6%.

C) 13.1%; 13.7%.

bmaggie

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) 12.8%; 13.6%.

C) 13.1%; 13.7%.

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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%.

bmaggie

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

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

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

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

bmaggie

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

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

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

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

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

bmaggie

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%.

bmaggie

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.

bmaggie

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) 18.4%.

B) 17.0%.

C) 19.0%.

bmaggie

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) 18.4%.

B) 17.0%.

C) 19.0%.

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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%.

zaestau

c

kison

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