Describe the distribution of ages of pennies (remember that the instruction “describe” means to
discuss center, spread, and shape). Justify your answer.
A wealthy woman is trying to decide whether or not to buy a coin collection that contains 1450
coins. She will buy the collection only if at least 225 of the coins are worth more than $170. The
present owner of the collection reports that the average coin in the collection is worth $130 with a
standard deviation of $15. Should the woman buy the collection?
- The mean of a set of 150 values is 35, its median is 33, its standard deviation is 6, and its IQR is 12.
A new set is created by first subtracting 10 from every term and then multiplying by 5. What are the
mean, median, variance, standard deviation, and IQR of the new set? - The following graph shows the distribution of the heights of 300 women whose average height is 65′′
and whose standard deviation is 2.5′′. Assume that the heights of women are approximately normally
distributed. How many of the women would you expect to be less than 5′2′′ tall? - Which of the following are properties of the standard deviation ? Explain your answer.
a. It’s the square root of the average squared deviation from the mean.
b. It’s resistant to extreme values.
c. It’s independent of the number of terms in the distribution.
d. If you added 25 to every value in the dataset, the standard deviation wouldn’t change.
e. The interval ± 2s contains 50% of the data in the distribution.
Look again at the salaries of the Golden State Warriors in problem 11 (in millions, 6.2, 5.4, 5.4, 4.9,
4.4, 4.4, 3.4, 3.3, 3.0, 2.4, 2.3, 1.3, .3, .3). Erick Dampier was the highest paid player at $6.2 million.
What sort of raise would he need so that his salary would be an outlier among these salaries?
- Given the histogram below, draw, as best you can, the boxplot for the same data.