SAT Prep on Statistics

If a distribution is skewed to the right with no outliers, 

• mean<median
• mean>median
• mean=median
• can not determine

Which of the following statements about this distribution is not correct?

• The histogram is skew right.
• The median is less than the $20.
• The IQR is $35.
• The mean is greater then the median. 

The scores on a statistics exam had a mean of 81 and a standard deviation of 9. One student was absent on the test day, and his score wasn't included in the calculation. If his score of 84 is added to the distribution of scores, what would happen to the mean and standard deviation?

• mean will increase, standard deviation will increase
• mean will increase, standard deviation will decrease
• mean will increase, standard deviation will stay the same
• mean will decrease, standard will decrease 

True or false: The IQR is a resistant measure of spread.

• True 
• False

A survey was designed to study how business operations vary according to their size. Companies were classified as small,medium, or large. Questionnaires were sent to 200 randomly selected businesses of each size. Because not all questionnaires in a survey of this type are returned, researchers decided to investigate the relationship between the response rate and the size of the business. The data are given in the following two-way table:
What percent of all small companies receiving questionnaires responded?

• 20.8%
• 33.3%
•  50.8%
•  62.5%

The mean salary of all female workers is $35,000. The mean salary of all male workers is $41,000. What must be true about the mean salary of all workers?

• It must be $38,000.
• It must be larger than the median salary.
• It could be any number between $35,000 and $41,000.
• It must be larger than $38,000.

Rain water was collected at 30 sites and the pH level was measured. The mean and standard deviation of values of 4.60 and 1.10, respectively. When the pH meter was recalibrated back at the laboratory, it was found to be an error. The error can be corrected by adding 0.1 pH units to all the values and then multiplying the result by 1.2. The mean and standard deviation of the corrected pH measurements are

• 5.64, 1.44
• 5.40, 1.44
• 5.64, 1.20
• 5.64, 1.32

If the heights of American men follow the Normal distribution, and 99.7% have heights between 5'0'' and 7'0'', what is your estimate of the standard deviation of the height of American men?

• 1"
• 3"
• 4"
• 6"

What is the standardized score (z-score) for a student who scored 500 on the old SAT scale?

• -30
• -0.13
• 0.13
• 0.27

Many professional schools require applicants to take a standardized test. Suppose that 1000 students take such a test. Several weeks after the test, Pete recieves his score report: he got a 63, which placed him at the 73rd percentile. This means that

• Pete's score was below the median.
• Pete did worse than about 63% of the test takers.
• Pete did worse than about 73% of the test takers.
• Pete did better than about 73% of the test takers.