Missy Walters owns a mail-order business specializing in baby clothes. She is considering offering her customers a discount on shipping charges based on the dollar-amount of the mail order. Before Missy decides the discount policy, she needs a better understanding of the dollar-amount distribution of the mail orders she receives. Missy had an assistant randomly select 50 recent orders and record the value, to the nearest dollar, of each order as shown below.
136 281 226 123 178 445 231 389 196 175
211 162 212 241 182 290 434 167 246 338
194 242 368 258 323 196 183 209 198 212
277 348 173 409 264 237 490 222 472 248
231 154 166 214 311 141 159 362 189 260
a. Determine the mean, median, and mode for this data set.
b. Determine the 80th percentile.
c. Determine the first quartile.
d. Determine the range and interquartile range.
e. Determine the sample variance, sample standard deviation, and coefficient of variation.
f. Determine and interpret the z-scores for the minimum and maximum values in the data set.