*****Please show me step by step on how to solve this question and answers. Than
ID: 3150273 • Letter: #
Question
*****Please show me step by step on how to solve this question and answers. Thank you.*****
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.
Explanation / Answer
a)for calculating mean add all the sample values and divide result with the number of observations.
mean=12573/50=251.46
for calculating median arrange the given sample data in increasing order from descending to ascending order. then calculate median using the formula:{n/2th observation+(n/2+1)/2th observation}/2.
123 136 141 154 159 162 166 167 173 175 178 182 183 189
194 196 196 198 209 211 212 212 214 222 226 231 231
237 241 242 246 248 258 260 264 277 281 290 311
323 338 348 362 368 389 409 434 445 472 490
25th observation=226
26th observation=231
median=(226+231)/2=228.5
for calculating mode, use this formula: mode=3*median-2*mean=3*228.5-2*251.46=685.5-502.92=182.58
b)80th percentile: 80/100*n=40th number is 80th percentile=323
c)median is 182.58, this leaves (123 136 141 154 159 162 166 167 173 175 178 182) 12 numbers below, so middle numbers are 162 and 166, average=162+166/2=164 is 1st quartile.
d) Range=maximum value-minimum value=490-123=367
e)variance: 1/n|xi-x bar|, where xi are the values of the sample and x bar is the mean
standard deviation:variance
coefficient of variation:standard deviation/mean*100%
f)while calculating range ou've already got the maximum and minimum values. i.e 490 and 123
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