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, 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

Ans :

Give data set are below :

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

a) Mode :The mode is the number that appears most frequently.

In our data 124 appears 2 times and 125 appears 2 times and rest of data values appears 1 time

Mode : 124 and 125

a data has bimodal

b) Ans :

ΣΧί Arithmetic mean η

mean = 1115 / 9

Arithmetic 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

arranging dat into ascending order

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

here total number of data value is 9

since odd number of data values in this data set, there is only one middle number

Median = 124

Since Median $\leq$ Mode

d) Ans :

Based on the values of the arithmetic mean, median, and mode

Arithmetic mean = 123.8889

median = 124

Mode is 124 and 125

since Mode > Median >arithmetic mean

this is positive skived distribution

125 124 Mode 123.88 Median Mean

e) Ans :

To compute standard deviation using following formula :

S= (E(Xi – X)^2 n - 1

S = (Σ(Xi – 123.8888)^2 9 - 1

$s=\sqrt{\frac{40.8888}{8}}$

s = 2.2607

Standard deviation of the sample

s = 2.2607