Question

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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, 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

a)

Mode: The mode is the number that appears most frequently. A data set may have multiple modes. If it has two modes, the data set is called bimodal. If all the data values have the same frequency, all the data values are modes. Here, two numbers 124 and 125 occured 2 times in data set so both are the modes. The modes are -

124,125

b)

3) arithmatic mean Arithmatic mean (X) Exi Sum of all observations Total number of observations 124 + 125 +123+120+124+127 + 125+ 126+ 121 9 N115 Arithmatic mean = 123.8889

c)

Median:

The median of a data set is found by putting the data set in ascending numerical order and identifying the middle number. If there are an odd number of data values in the data set, the median is a single number. If there are an even number of data values in the data set, the median is the average of the two middle numbers. Sorting the data set for the values entered above we have:

120,121,123,124,124,125,125,126,127

Since there is an odd number of data values in this data set, there is only one middle number. With 9 data values, the middle number is the data value at position 5. Therefore, the median is 124.

d) here, mean = 123.8889 , median = 124, mode = 124, 125

Hence mean < median < mode.

So distribution is negatively skewed. I.e shape of the distribution is negatively skewed.

e) standard deviation-

e) standard deviation - S = Elxi-x) 2 401888 9 n-) 9-) S = 15.1 S = 2.26077

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