Question

Etsy is an e-commerce website focused on handmade or vintage items and supplies, as well as unique factory-manufactured items. A shop owner on Etsy sells printed t-shirts and she wants to know what level of inventory she should maintain for the month of January. She gathers the January inventories of 8 other shop owners who sell printed t-shirts on Etsy. Their t-shirt inventories are listed below.

Use these data to answer the following questions. 59 84 90 54 42 45 77 85

(a) Calculate the mean inventory of the Etsy shop owners.

(b) Calculate the median inventory value for the Etsy shop owners.

(c) Fill in the blank Suppose the shop owner with the highest inventory in the data above actually had an inventory of 100 t-shirts. The mean score of the eight shop owners would . The median inventory of the eight shop owners would . We conclude that the is robust to extreme observations based on the first two answers. Note: 100 replaces the highest value in the previous data set. i. stay the same, increase, median ii. increase, decrease, median iii. increase, stay the same, mean iv. increase, stay the same, median v. increase, increase, median

(d) The variance of the eight scores is 369.1429. Calculate the standard deviation. Round your final answer to four decimal places.

(e) Which quartile does the answer in part (b) correspond to?

(f) Given your answers to parts (a) and (b), what can we say about the shape of the distribution of Etsy shop owner’s t-shirt inventory?

Answer 1

Explanation:

given that Etsy is an e-commerce website focused on handmade or vintage items and supplies, as well as unique factory-manufactured items. A shop owner on Etsy sells printed t-shirts and she wants to know what level of inventory she should maintain for the month of January. She gathers the January inventories of 8 other shop owners who sell printed t-shirts on Etsy. Their t-shirt inventories are listed below.

59 84 90 54 42 45 77 85

a) Mean = total /8 = 536/8 = 67

For median arrange in ascending order

42 45 54 59 77 84 85 90

Middle entries are 59 and 77

b) Median = average of 59 and 77 = 68

c) If highest changes to 100, data set becomes

42 45 54 59 77 84 85 100

sum increases by 10 i.e. 546

Mean = 546/8 = 68.25

Median will not change remain the same = 68

Mean increases and median stays the same

d) If Var = 369.1429

std dev = square root of variance

= 19.2131

e) Part b answer is the II quartile

f) Mean = 67 and median = 68

Mean < median

So negatively skewed shape