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Interquartile range and outliers

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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. Interquartile range of eleven values ●○○○○ 10 ptsFind the interquartile range of the data set 21, 23, 20, 27, 25, 24, 30, 21, 22, 28, 30.
3. 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.
4. Outlier percentage in a normal distribution ●●○○○ 20 ptsIn a normal distribution, a value is an outlier if it lies more than $1.5$ interquartile ranges above the upper quartile or more than $1.5$ interquartile ranges below the lower quartile. Using $z=\pm 0.67$ for the quartiles, what percent of values are outliers under this definition? Give the percent rounded to two decimal places.
5. Interquartile range from a frequency table ●●○○○ 20 ptsA survey records the number of people in each car passing a particular point. The frequency of each number of people in a car is: - 1 person: 45 cars - 2 people: 198 cars - 3 people: 121 cars - 4 people: 76 cars - 5 people: 52 cars - 6 people: 13 cars Find the interquartile range of the number of people in a car.
6. 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 $Q_3+1.5\cdot IQR$.

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