Problem #1. The performance time (minutes) for Beethoven's Ninth symphony is obtained from each of the six compact discs.

67 64 71 69 75 68

Please show your work as much as possible for the following sub-questions. (Round your answers to 2 decimal places if necessary, e.g., 12.34.)

(i). Calculate the mean.

(ii). Calculate the standard deviation.

(iii). Suppose one more observation has been added to the existing data. With this new observation, the mean becomes 70. What is the value of the new observation?

Problem #2. A zoologist collected wild lizards in the Southwestern United States. Two groups of lizards, with 8 and 11 observations, from the genusPhrynosomawere placed on a treadmill, and their speed measured. The recorded speed (meters/second) is the fastest time to run a half meter.

Group I 1.28 1.36 1.24 2.47 1.94 2.52 2.67 1.29 1.56 2.66 2.17 Groupe II 1.57 2.10 2.54 1.63 2.11 2.57 1.72 0.36

Please show your work as much as possible for the following sub-questions.

(i). Provide the five-number summary for Group I.

(ii). Provide the five-number summary for Group II.

(iii). Draw side-by-side box plots for Groups I and II. (Draw two box plots in the same horizontal line so that you can compare those.)

(iv). Comment on the shapes of the distributions.

1

Problem #3. The 50 measurements of acid rain in Wisconsin are as follows:

3.58 3.8 4.01 4.01 4.05 4.05 4.12 4.18 4.2 4.21

4.27 4.28 4.3 4.32 4.33 4.35 4.35 4.41 4.42 4.45

4.45 4.5 4.5 4.5 4.5 4.51 4.52 4.52 4.52 4.57

4.59 4.6 4.61 4.61 4.62 4.62 4.65 4.7 4.7 4.7

4.7 4.72 4.78 4.78 4.8 5.07 5.2 5.26 5.41 5.48

Please show your work as much as possible for the following sub-questions.

(i). Find the 13th percentile.

(ii). Find the 39th percentile.

(iii). Find the 60th percentile.

(iv). Roughly, how many observations would fall between the 13th percentile and the 79th percentile? (Note that this can be solved without getting the actual percentile values.)

Problem #4. Miles wrote down a table to calculate the variance of data, which consists of positive obser vations. However, he mistakenly spilled his coffee, so some of the numbers on the table became no more recognizable. Fortunately, he knows the mean of the data is 4.

x x²x x (x x)²

#1 2 ! ! !

#2 ! ! ! !

#3 ! 9 ! !

#4 ! ! 6 !

Total ! ! ! !

(i). Help him to recover the lost numbers in the above table.

(ii). Calculate the variance. (Round your answers to 2 decimal places if necessary, e.g., 12.34.)