Question

Rainbow Trout, Inc. feeds fingerling trout in special ponds and markets them when they attain a certain weight. A sample of 9 trouts were isolated in a pond and fed a special food mixture called “Grow Em Fast”. At the end of the experimental period, the weights of the trouts were (in grams): 124, 125, 123, 120, 124, 127, 125, 126 and 121.

a) What is the mode? Justify properly your answer. (1 mark)

b) What is the arithmetic mean? (2 marks)

c) What is the median? Justify properly your answer. (2 marks)

d) Based on the values of the arithmetic mean, median, and mode, what is the most likely shape of the distribution? Justify properly your answer. (1 mark)

e) Compute the standard deviation of the sample. (4 marks)

Answer 1

We have Sample 124,128,123,120, 124, 127, 125, 126, 121 n=9 o) Mode: The observation occute's maximum time 124 and 125 OCLES Manimum time these for This is simodell with Modes 124, 125 o We have b) Azithmatic mean (*) hods = 123.8889 Alithmatic mean is 123.89 T = Ixi c) Mellon! Plidare most abseerashion Let creang duter in increasing ordag 120,121, 123, 124, 124, 125, 125, 126, 127 Mediun = vale a (ntly obsn a Valle on ( 211 obst Valven 5th obsh = 124 Median is 124 for shape d) We use skeconegs distribution fince it Mean is gepake than median the distribution is positively dreved if mean is less than median the distribution is neqatively Skewed Hege. 123.89<134 ve. Mean< Median Therefore Mast Jikely shape of distribution to negatively skewed es from given dator We have , IxiL 183177 , IX= !!! , n=9 10.89 107 Standard deviation 11152 138177- [x²_ (5x35 2.2608 ni ga 2.2608 Standard deviation is CS Scanned with CamScanner