Distributions of Data

For the density curve above, which of the following is true?

• The median is 0.5.
  

• The median is larger than 0.5.
  

• The density curve is skewed right.
  

• The density curve is Normal.
  

For this density curve, what percent of the observations lie above 4?

• 20%

• 25%

• 50%

• 75%

You can roughly locate the mean of a density curve by eye because it is...

• the point at which the curve would balance if made of solid material.

• the point that divides the area under the curve into two equal parts.

• the point at which the curve reaches its peak.

• the point where the curvature changes direction.

You can roughly locate the median of a density curve by eye because it is...

• the point at which the curve would balance if made of solid material.

• the point that divides the area under the curve into two equal parts.

• the point at which the curve reaches its peak.

• the point where the curvature changes direction.

You are told that your score on an exam is at the 85 percentile of the distribution of scores.
Which of the following is a correct interpretation of this information?

• Your score was lower than approximately 85% of the people who took this exam.

• Your score was higher than approximately 85% of the people who took this exam.

• You answered 85% of the questions correctly.

• 85% of the people who took this test earned the same score you did.

Here is a list of exam scores for the 14 students in Mr. Williams’s calculus class:
60   61   61   65   72   75   75  
78   81   81   85   89    91   98
What is the percentile of the person whose score was 85?

• 21%

• 29%

• 71%

• 85%

An ecologist who was studying starfish populations collected starfish of the species Pisaster was interested in the distribution of sizes of starfish on a certain shoreline.  One measure of size is “arm length.”  Above is a cumulative relative frequency distribution for the arm length of 102 Pisaster individuals.
The median and interquartile range of this distribution are approximately:

• Median is 15.2; Intequartile range is 12.5 to 16.2

• Median is 13; Interquartile range is 3.1

• Median is 13; Intequartile range is 3.7

• Median is 15.2; Intequartile range is 3.7

A standard score describes...

• How much spread there is in a distribution

• How far apart the mean and median of a distribution are.

• How far a particular score is from the mean.

• How far a particular score is from the median.

The distribution of household incomes in a small town is strongly skewed to the right.  The mean income is $42,000 and the standard deviation is $24,000.  The Ames family’s household income is $60,000. 
The z-score for the Ames family’s
income is...

• -0.75

• 0.3

• 0.75

• 0.86

Ramon is planning on buying a new car.  He’s looking at the Ford Escape—a sport-utility vehicle—which gets 28 highway miles per gallon, and the Ford Fusion—a mid-sized sedan—which gets 31 highway miles per gallon.   The mean fuel efficiency for all sport utility vehicles is 23, with a standard deviation of 7.6.  The mean of all mid-sized sedans is 27, with a standard deviation of 5.2. Which vehicle has a better standing, relative to others of the same style?

• The Ford Fusion sedan has a better relative standing, because it’s z-score is higher

• The Ford Fusion sedan has a better relative standing., because it’s z-score is closer to 0.

• The Ford Escape SUV has a better relative standing, because it’s z-score is higher

• The Ford Escape SUV has a better relative standing, because it’s z-score is closer to 0.