Check each data set for outliers.

a. $14,18,27,26,19,13,5,25$ b. $112,157,192,116,153,129,131$

Check each data set for outliers.

a. $506,511,517,514,400,521$ b. $3,7,9,6,8,10,14,16,20,12$

Consider the following data.

$$\begin{array}{llll} 14 & 24 & 18 & 22 \\ 19 & 18 & 16 & 22 \\ 24 & 17 & 15 & 16 \\ 19 & 23 & 24 & 16 \\ 16 & 26 & 21 & 16 \\ 20 & 22 & 16 & 12 \\ 24 & 23 & 19 & 25 \\ 20 & 25 & 21 & 19 \\ 21 & 25 & 23 & 24 \\ 22 & 19 & 20 & 20 \end{array}$$

Develop a frequency distribution using classes of 12–14, 15–17, 18–20, 21–23, and 24–26.

Eleanor scores 680 on the mathematics part of the SAT. The distribution of SAT scores in a reference population is normal, with mean 500 and standard deviation 100. Gerald takes the American College Testing (ACT) mathematics test and scores 27. ACT scores are normally distributed with mean 18 and standard deviation 6. Find the standardized scores for both students. Assuming that both tests measure the same kind of ability, who has the higher score?

Eleanor scores 680 on the SAT Mathematics test. The distribution of SAT Math scores is symmetric and single-peaked with mean 500 and standard deviation 100. Gerald takes the American College Testing (ACT) Mathematics test and scores 29. ACT scores also follow a symmetric, single-peaked distribution-but with mean 21 and standard deviation 5. Find the standardized scores for both students. Assuming that both tests measure the same kind of ability, who has the higher score?

Police Calls in Schools The number of incidents in which police were needed for a sample of $9$ schools in Allegheny County is $7, 37, 3,8, 48, 11, 6, 0,10 .$ Find the first and third quartiles for the data.

Eleven major earthquakes had Richter magnitudes as shown. Find the first and third quartiles for the data.

$$7.0,6.2,7.7,8.0,6.4,6.2,7.2,5.4,6.4,6.5,7.2$$

Achievement Test Scores The data shown represent the scores on a national achievement test for a group of $10$ th-grade students. Find the approximate percentile ranks of these scores by constructing a percentile graph.

$$\begin{array}{lc} \textbf{Score} & \textbf{Frequency} \\ \hline 196.5-217.5 & 5 \\ 217.5-238.5 & 17 \\ 238.5-259.5 & 22 \\ 259.5-280.5 & 48 \\ 280.5-301.5 & 22 \\ 301.5-322.5 & 6 \end{array}$$

$$276$$

Achievement Test Scores The data shown represent the scores on a national achievement test for a group of $10$ th-grade students. Find the approximate percentile ranks of these scores by constructing a percentile graph.

$$\begin{array}{lc} \textbf{Score} & \textbf{Frequency} \\ \hline 196.5-217.5 & 5 \\ 217.5-238.5 & 17 \\ 238.5-259.5 & 22 \\ 259.5-280.5 & 48 \\ 280.5-301.5 & 22 \\ 301.5-322.5 & 6 \end{array}$$

$$245$$

Achievement Test Scores The data shown represent the scores on a national achievement test for a group of $10$ th-grade students. Find the approximate percentile ranks of these scores by constructing a percentile graph.

$$\begin{array}{lc} \textbf{Score} & \textbf{Frequency} \\ \hline 196.5-217.5 & 5 \\ 217.5-238.5 & 17 \\ 238.5-259.5 & 22 \\ 259.5-280.5 & 48 \\ 280.5-301.5 & 22 \\ 301.5-322.5 & 6 \end{array}$$

$$280$$

A random selection of state gasoline taxes per gallon is given below. Find the first and third quartile values for the data.

$$\begin{array}{lllllllll}16 & 18 & 35.3 & 25 & 23.5 & 27.1 & 32.5 & 16 & 22\end{array}$$

$$\begin{array}{lllll}17.5 & 19 & 29.5 & 7.5 & 12\end{array}$$

Test Scores Find the percentile rank for each test score in the data set. \

$$12,28,35,42,47,49,50$$

What value corresponds to the $60$ th percentile?

Achievement Test Scores The data shown represent the scores on a national achievement test for a group of $10$ th-grade students. Find the approximate percentile ranks of these scores by constructing a percentile graph.

$$\begin{array}{lc} \textbf{Score} & \textbf{Frequency} \\ \hline 196.5-217.5 & 5 \\ 217.5-238.5 & 17 \\ 238.5-259.5 & 22 \\ 259.5-280.5 & 48 \\ 280.5-301.5 & 22 \\ 301.5-322.5 & 6 \end{array}$$

$$300$$

Achievement Test Scores The data shown represent the scores on a national achievement test for a group of $10$ th-grade students. Find the approximate percentile ranks of these scores by constructing a percentile graph.

$$\begin{array}{lc} \textbf{Score} & \textbf{Frequency} \\ \hline 196.5-217.5 & 5 \\ 217.5-238.5 & 17 \\ 238.5-259.5 & 22 \\ 259.5-280.5 & 48 \\ 280.5-301.5 & 22 \\ 301.5-322.5 & 6 \end{array}$$

$$220$$