Exam 3: Statistics for Describing, Exploring, and Comparing Data

Construct a modified boxplot for the data. -The weights (in ounces)of 27 tomatoes are listed below. Construct a modified boxplot for the data. 1.7 2.0 2.2 2.2 2.4 2.5 2.5 2.5 2.6 2.6 2.6 2.7 2.7 2.7 2.8 2.8 2.8 2.9 2.9 2.9 3.0 3.0 3.1 3.1 3.3 3.6 4.2

Determine which score corresponds to the higher relative position. -Which score has the highest relative position: a score of 36 on a test for which $x = 26$ and $s = 10$ , a score of $5.6$ on a test for which $\bar { x } = 4.6$ and $s = 0.8$ or a score of 468 on a test for which $\bar { x } = 413$ and $s = 50$ ?

Find the median for the given sample data. --20, -27, -46, -27, -49, -27, -49

Provide an appropriate response. -Heights of adult women are known to have a bell-shaped distribution. Draw a boxplot to illustrate the results.

Solve the problem. -When data are summarized in a frequency distribution, the median can be found by first identifying the median class (the class that contains the median). We then assume that the values in that class are evenly distributed and we can interpolate. This process can be described by $\text { median } = ( \text { lower limit of median class } ) + ( \text { class width } ) \left( \frac { \frac { \mathrm { n } + 1 } { 2 } - ( \mathrm { m } + 1 ) } { \text { frequency of median class } } \right)$ where n is the sum of all class frequencies and m is the sum of the class frequencies that precede the median class. Use this procedure to find the median of the frequency distribution below: Score Frequency 50-59 21 60-69 24 70-79 22 80-89 16 90-99 17

Solve the problem. -The signal-to-noise ratio of a set of data is obtained by dividing the mean by the standard deviation. Find the signal-to-noise ratio for the following sample of weights (in pounds): 144 125 186 105 197 136 172 155 116 125

Solve the problem. -Construct a data set for which the range is misleading as a measure of variation. Explain why the range is misleading and suggest an alternative measure of variation.

If all the values in a data set are converted to z-scores, the shape of the distribution of the z-scores will be the same as the distribution of the original data.

Find the midrange for the given sample data. -Compute the variance. Jeanne is currently taking college zoology. The instructor often gives quizzes. On the past five quizzes, Jeanne got the following scores: 11 11 10 10 13