the dataset, it is the end of the upper whisker, as shown in the following diagram:
A distribution is strongly skewed to the right. Would you prefer to use the mean and standard
deviation, or the median and interquartile range, to describe the center and spread of the distribution?
Answer: Because the mean is not resistant and is pulled toward the tail of the skewed distribution,
you would prefer to use the median and IQR.
- A distribution is strongly skewed to the left (like a set of scores on an easy quiz) with a mean of 48
and a standard deviation of 6. What can you say about the proportion of scores that are between 40
and 56?
Answer : Since the distribution is skewed to the left, we can’t say much. We could get a rough
estimate if we use Chebyshev’s rule. We note that the interval given is the same distance (8) above
and below = 48. Solving 48 + k (6) = 56 gives k = 1.33. Hence, there are at least
of the scores between 40 and 56.
Practice Problems
Multiple-Choice
The following list is ordered from smallest to largest: 25, 26, 26, 30,y, y, y , 33, 150. Which of the
following statements is (are) true?
I. The mean is greater than the median
II. The mode is 26
III. There are no outliers in the data
a. I only
b. I and II only
c. III only
d. I and III only
e. II and III only
- Jenny is 5′10′′ tall and is wondering about her height. The heights of girls in the school are
approximately normally distributed with a mean of 5′5′′ and a standard deviation of 2.6′′. What is the
percentile rank of Jenny’s height?
a. 59
b. 65