91Ó°ÊÓ

The following data give the hourly wage rates of eight employees of a company. \(\begin{array}{lllllll}\$ 22 & 22 & 22 & 22 & 22 & 22 & 22\end{array}\) 22 Calculate the standard deviation. Is its value zero? If yes, why?

Are the values of the mean and standard deviation that are calculated using grouped data exact of approximate values of the mean and standard deviation, respectively? Fxplain.

The following table gives the frequency distribution of the number of errors committed by a college baseball team in all of the 45 games that it played during the \(2011-12\) season. \begin{tabular}{cc} \hline Number of Errors & Number of Games \\ \hline 0 & 11 \\ 1 & 14 \\ 2 & 9 \\ 3 & 7 \\ 4 & 3 \\ 5 & 1 \\ \hline \end{tabular} Find the mean, variance, and standard deviation. (Hint: The classes in this example are single valued. These values of classes will be used as values of \(m\) in the formulas for the mean, variance, and standard deviation.)

Briefly describe how the three quartiles are calculated for a data set. Illustrate by calculating the three quartiles for two examples, the first with an odd number of observations and the second with an even number of observations.

Explain the concept of the percentile rank for an observation of a data set.

The following data give the weights (in pounds) lost by 15 members of a health club at the end of 2 months after joining the club. \(\begin{array}{rrrrrrrr}5 & 10 & 8 & 7 & 25 & 12 & 5 & 14 \\ 11 & 10 & 21 & 9 & 8 & 11 & 18 & \end{array}\) a. Compute the values of the three quartiles and the interquartile range. b. Calculate the (approximate) value of the 8 2nd percentile. c. Find the percentile rank of \(10 .\)

The following data give the numbers of text messages sent by a high school student on 40 randomly selected days during 2012: \(\begin{array}{llllllllll}32 & 33 & 33 & 34 & 35 & 36 & 37 & 37 & 37 & 37 \\\ 38 & 39 & 40 & 41 & 41 & 42 & 42 & 42 & 43 & 44 \\ 44 & 45 & 45 & 45 & 47 & 47 & 47 & 47 & 47 & 48 \\ 48 & 49 & 50 & 50 & 51 & 52 & 53 & 54 & 59 & 61\end{array}\) a. Calculate the values of the three quartiles and the interquartile range. Where does the value 49 fall in relation to these quartiles? b. Determine the approximate value of the 91 st percentile. Give a brief interpretation of this percentile. c. For what percentage of the days was the number of text messages sent 40 or higher? Answer by finding the percentile rank of 40 .

Prepare a box-and-whisker plot for the following data: \(\begin{array}{llllllll}36 & 43 & 28 & 52 & 41 & 59 & 47 & 61 \\ 24 & 55 & 63 & 73 & 32 & 25 & 35 & 49 \\ 31 & 22 & 61 & 42 & 58 & 65 & 98 & 34\end{array}\) Does this data set contain any outliers?

The heights of five starting players on a basketball team have a mean of 76 inches, a median of 78 inches, and a range of 11 inches. a. If the tallest of these five players is replaced by a substitute who is 2 inches taller, find the new mean, median, and range. b. If the tallest player is replaced by a substitute who is 4 inches shorter, which of the new values (mean, median, range) could you determine, and what would their new values be?

In the Olympic Games, when events require a subjective judgment of an athlete's performance, the highest and lowest of the judges' scores may be dropped. Consider a gymnast whose performance is judged by seven judges and the highest and the lowest of the seven scores are dropped. a. Gymnast A's scores in this event are \(9.4,9.7,9.5,9.5,9.4,9.6\), and \(9.5\). Find this gymnast's mean score after dropping the highest and the lowest scores. b. The answer to part a is an example of (approximately) what percentage of trimmed mean? c. Write another set of scores for a gymnast \(B\) so that gymnast \(A\) has a higher mean score than gymnast B based on the trimmed mean, but gymnast B would win if all seven scores were counted. Do not use any scores lower than \(9.0\).