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1. Quartiles of an eight-value data set ●○○○○ 10 ptsFor the data $12, 14, 17, 20, 21, 21, 21, 26$, find the lower quartile $Q_1$, the upper quartile $Q_3$ and the interquartile range. Split the data into lower and upper halves at the median.
2. IQR of a six-value data set ●○○○○ 10 ptsFind the interquartile range (IQR) of the data set 4, 7, 9, 11, 12, 20. Use the median of the lower half for $Q_1$ and the median of the upper half for $Q_3$, leaving out the middle value when the count is odd.
3. Fifth decile of fund growth rates ●○○○○ 10 ptsA mutual fund achieved the following monthly growth rates (in percent) over an 11-month period: 3, 2, 7, 8, 2, 4, 3, 7.5, 7.2, 2.7, 2.09. Determine the 5th decile of the data (give the value in percent, without the % sign).
4. Range of a five-integer set ●●○○○ 20 ptsA set of five positive integers has mean 5, median 5, and 8 as its only mode. What is the difference between the largest and smallest integers in the set?
5. Largest integer in a five-number list ●●○○○ 20 ptsA list of five positive integers has all of the following properties: - The only integer in the list that occurs more than once is $8$. - Its median is $9$. - Its average (mean) is $10$. What is the largest possible integer that could appear in the list?
6. Median of consecutive integer sets ●●○○○ 20 ptsLet $a$, $b$, and $c$ be integers with $a < b < c$. Let $S$ be the set of all integers from $a$ to $b$, inclusive, and $Q$ the set of all integers from $b$ to $c$, inclusive. The median of $S$ is $\frac{3}{4}b$ and the median of $Q$ is $\frac{7}{8}c$. Let $R$ be the set of all integers from $a$ to $c$, inclusive. What fraction of $c$ is the median of $R$? Give your answer as a decimal.
7. Finding an outlier with the IQR rule ●●○○○ 20 ptsFor the data set $15, 17, 19, 16, 14, 58$, find the outlier using the quartiles (the median of each half of the data) and the rule that a value is an outlier if it lies below $Q_1-1.5\cdot IQR$ or above $Q_3+1.5\cdot IQR$.
8. Medians of a triangle in space ●●○○○ 20 ptsTriangle $ABC$ has vertices $A(0, 0, 6)$, $B(0, 4, 0)$ and $C(6, 0, 0)$. Find the lengths of the three medians of the triangle. Give each length rounded to two decimal places, listed in increasing order.
9. Greatest integer after adding four ●●●○○ 50 ptsFour integers are added to the group of integers 3, 4, 5, 5 and 8. As a result, the mean, the median and the mode of the data each increase by 1. What is the greatest integer in the new group of integers?