Please show me step by step on how to solve this question an

*****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.

Solution

Ordering the data from smallest to largest,

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

a)

Mean = Sum(x) / N = 251.46
Median = (25th term + 26th term)/2 = (226+231)/2 = 228.5
Mode = most number of occurrences = 196 [answer]

*******************

As 80% of 50 = 40, then the 80th percentile = 41st term (40 terms must be lower than it)

b) 80th percentile = 41st term = 323 [answer]

*****************

c) Q1 = median of lower half = 13th term = 183

*****************

d)

Range= max - min = 490 - 123 = 367 [answer]

Q3 = median of upper half = 38th term = 290

Thus,

IQR = Q3 - Q1 = 290 - 183 = 107 [answer]

***************************

Hi! Please submit the next part as a separate question. That way we can continue helping you! Thanks!