Consumer Reports posts reviews and ratings of a variety of products on its website. The following is

Question:

Consumer Reports posts reviews and ratings of a variety of products on its website. The following is a sample of 20 speaker systems and their ratings. The ratings are on a scale of 1 to 5, with 5 being best.

Speaker Rating Speaker Rating Infinity Kappa 6.1 4.00 ACI Sapphire III 4.67 Allison One 4.12 Bose 501 Series 2.14 Cambridge Ensemble II 3.82 DCM KX-212 4.09 Dynaudio Contour 1.3 4.00 Eosone RSF1000 4.17 Hsu Rsch. HRSW12V 4.56 Joseph Audio RM7si 4.88 Legacy Audio Focus 4.32 Martin Logan Aerius 4.26 Mission 73li 4.33 Omni Audio SA 12.3 2.32 PSB 400i 4.50 Polk Audio RT12 4.50 Snell Acoustics D IV 4.64 Sunfire True Subwoofer 4.17 Thiel CS1.5 4.20 Yamaha NS-A636 2.17

a. Compute the mean and the median.

b. Compute the first and third quartiles.

c. Compute the standard deviation.

d. The skewness of this data is 1.67. Comment on the shape of the distribution.

e. What are the z-scores associated with Allison One and Omni Audio?

f. Do the data contain any outliers? Explain.

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