Question

Problem 6 (10 marks) 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, 118, 125, 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

solution, n=9 x2 124 15376 125 15625 123 118 125 15129 13924 15625 16129 15625 127 125 126 121 15876 14641 137950 Sum 1114 Sample mean x 124+. + 121 1114 9 123.778 9 sample vaiance š = (2xi>= + (2xi)) (137950 1 9-1 9 7.694 standard deviation s = = /s² = 17.694 2.774 Here the median, Data set. 118, 121,123,124, 125, 125, 125, 126, 127 median - ntl nt 9+1 - 5 median 5th 125 Here the mode, mode: The most repeated observation mode = 125, appeared 3 times