Answer: Bimodal, somewhat skewed to the left.
For the graph of problem #1, would you expect the mean to be larger than the median or the median to
be larger than the mean? Why?
Answer: It is difficult to predict. The general guideline that the mean is lower than the median for
distributions that are skewed left applies to smooth unimodal distributions. Bimodal distributions
don’t necessarily follow that pattern.
- The first quartile (Q1) of a dataset is 12 and the third quartile (Q3) is 18. What is the largest value
above Q3 in the dataset that would not be a potential outlier?
Answer: Outliers lie more than 1.5 IQRs below Q1 or above Q3. Q3 + 1.5(IQR) = 18 + 1.5(18 – 12)
= 27. Any value greater than 27 would be an outlier. 27 is the largest value that would not be a
potential outlier. - A distribution of quiz scores has = 35 and s = 4. Sara got 40. What was her z -score? What
information does that give you if the distribution is approximately normal?
Answer :
This means that Sara’s score was 1.25 standard deviations above the mean, which puts it at the 89.4th
percentile (normalcdf(-100,1.25)).
In a normal distribution with mean 25 and standard deviation 7, what proportion of terms are less
than 20?
Answer : Area = 0.2389.(By calculator: normalcdf(-100, 20, 25, 7)=0.2375. )
What are the mean, median, mode, and standard deviation of a standard normal curve?
Answer: Mean = median = mode = 0. Standard deviation = 1.
Find the five-number summary and draw the modified box plot for the following set of data: 12, 13,
13, 14, 16, 17, 20, 28.
Answer: The five-number summary is [12, 13, 15, 18.5, 28]. 28 is an outlier (anything larger than
18.5 + 1.5(18.5 – 13) = 26.75 is an outlier by the 1.5(IQR) rule). Since 20 is the largest nonoutlier in